System and method for a mass flow controller

ABSTRACT

A system and method for controlling a mass flow controller to have a constant control loop gain under a variety of different types of fluids and operating conditions, and for configuring the mass flow controller for operation with a fluid and/or operating conditions different from that used during a production of the mass flow controller. Further, the system and method includes providing control by reducing the effects of hysteresis in solenoid actuated devices by providing a non-operational signal to the solenoid actuated device.

This application is a divisional of co-pending U.S. patent applicationSer. No. 10/131,603, filed Apr. 24, 2002, entitled “SYSTEM AND METHODFOR A MASS FLOW CONTROLLER” by John Michael Lull, et al., which is nowallowed, and which claims the benefit under 35 U.S.C. §119 (e) to U.S.provisional patent application Ser. No. 60/285,801, entitled “SYSTEM ANDMETHOD FOR A MASS FLOW CONTROLLER,” filed Apr. 24, 2001, each of whichis incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to a method and system forcontrolling the flow rate of a fluid, and more particularly to a massflow controller that can be configured for use with arbitrary processfluids and/or process operating conditions that may differ from thoseused during production of the mass flow controller.

BACKGROUND OF THE INVENTION

Many industrial processes require precise control of various processfluids. For example, in the pharmaceutical and semiconductor industries,mass flow controllers are used to precisely measure and control theamount of a process fluid that is introduced to a process chamber. Theterm fluid is used herein to describe any type of matter in any statethat is capable of flow. It is to be understood that the term fluidapplies to liquids, gases, and slurries comprising any combination ofmatter or substance to which controlled flow may be of interest.

Conventional mass flow controllers generally include four main portions:a flow meter, a control valve, a valve actuator, and a controller. Theflow meter measures the mass flow rate of a fluid in a flow path andprovides a signal indicative of that flow rate. The flow meter mayinclude a mass flow sensor and a bypass. The mass flow sensor measuresthe mass flow rate of fluid in a sensor conduit that is fluidly coupledto the bypass. The mass flow rate of fluid in the sensor conduit isapproximately proportional to the mass flow rate of fluid flowing in thebypass, with the sum of the two being the total flow rate through theflow path controlled by the mass flow controller. However, it should beappreciated that some mass flow controllers may not employ a bypass, assuch, all of the fluid may flow through the sensor conduit.

In many mass flow controllers, a thermal mass flow sensor is used thatincludes a pair of resistors that are wound about the sensor conduit atspaced apart positions, each having a resistance that varies withtemperature. As fluid flows through the sensor conduit, heat is carriedfrom the upstream resistor toward the downstream resistor, with thetemperature difference being proportional to the mass flow rate of thefluid flowing through the sensor conduit and the bypass.

A control valve is positioned in the main fluid flow path (typicallydownstream of the bypass and mass flow sensor) and can be controlled(e.g., opened or closed) to vary the mass flow rate of fluid flowingthrough the main fluid flow path and provided by the mass flowcontroller. The valve is typically controlled by a valve actuator,examples of which include solenoid actuators, piezoelectric actuators,stepper actuators, etc.

Control electronics control the position of the control valve based upona set point indicative of the mass flow rate of fluid that is desired tobe provided by the mass flow controller, and a flow signal from the massflow sensor indicative of the actual mass flow rate of the fluid flowingin the sensor conduit. Traditional feedback control methods such asproportional control, integral control, proportional-integral (PI)control, derivative control, proportional-derivative (PD) control,integral-derivative (ID) control, and proportional-integral-derivative(PID) control are then used to control the flow of fluid in the massflow controller. In each of the aforementioned feedback control methods,a control signal (e.g., a control valve drive signal) is generated basedupon an error signal that is the difference between a set point signalindicative of the desired mass flow rate of the fluid and a feedbacksignal that is related to the actual mass flow rate sensed by the massflow sensor.

Many conventional mass flow controllers are sensitive to componentbehavior that may be dependent upon any of a number of operatingconditions including fluid species, flow rate, inlet and/or outletpressure, temperature, etc. In addition, conventional mass flowcontrollers may exhibit certain non-uniformities particular to acombination of components used in the production of the mass flowcontroller which can result in inconsistent and undesirable performanceof the mass flow controller.

To combat some of these problems, a mass flow controller may be tunedand/or calibrated during production. Production generally includesoperating the mass flow controller on a test fluid under a set ofoperating conditions and tuning and/or calibrating the mass flowcontroller so that it exhibits satisfactory behavior.

As known to those skilled in the art, the tuning and/or calibration of amass flow controller is an expensive, labor intensive procedure, oftenrequiring one or more skilled operators and specialized equipment. Forexample, the mass flow sensor portion of the mass flow controller may betuned by running known amounts of a known fluid through the sensorportion and adjusting certain filters or components to provide anappropriate response. A bypass may then be mounted to the sensor, andthe bypass tuned with the known fluid to reflect an appropriatepercentage of the fluid flowing in the main fluid flow path at variousknown flow rates. The mass flow sensor portion and bypass may then bemated to the control valve and control electronics portions and thentuned again, under known conditions.

When the type of fluid used by an end-user differs from that used intuning and/or calibration, or when the operating conditions, such asinlet and outlet pressure, temperature, range of flow rates, etc., usedby the end-user differ from that used in tuning and/or calibration, theoperation of the mass flow controller can be expected to degrade. Forthis reason, additional fluids (termed “surrogate fluids”) and oroperating conditions are often tuned or calibrated, with any changesnecessary to provide a satisfactory response being stored in a lookuptable.

Although the use of additional tuning and/or calibration with differentfluids and at different operating conditions can be used to improve theperformance of the mass flow controller, this type of surrogate tuningand/or calibration is time consuming and expensive, as the tuning and/orcalibration procedures must be repeated for at least each surrogatefluid and likely must be repeated for a number of different operatingconditions with each surrogate fluid. Furthermore, because the surrogatefluids only approximate the behavior of the various types of fluids thatmay be used by the end-user, the actual operation of the mass flowcontroller at an end-user site may differ substantially from that duringtuning and/or calibration. Considering the wide range of industries andapplications employing mass flow controllers, the process fluid andoperating conditions applied to the mass flow controller by an end userare likely to be different than the test fluids and operating conditionsupon which a mass flow controller was tuned and/or calibrated, despitetuning and/or calibration of the mass flow controller with a number ofdifferent surrogate fluids and operating conditions.

In addition to the foregoing external factors (e.g., fluid species, flowrate, inlet and/or outlet pressure, temperature, etc.) that may affectthe performance and response of a mass flow controller, factorsassociated with the physical operation of a mass flow controller mayalso contribute to the overall sensitivity of the mass flow controllerto external factors and changing conditions. For example, many valvesemployed to control flow in mass flow controllers are solenoid actuateddevices.

Although a number of manufacturers of mass flow controllers utilizepiezoelectric actuators, solenoid actuators are generally preferred dueto their simplicity, their quick response, and their low cost.Nonetheless, solenoid actuated control valves do have certain drawbacks,with one of the more significant drawbacks of solenoid actuated controlvalves (and solenoid actuated devices in general) being that theyexhibit hysteresis. Hysteresis is a well known phenomenon common to manyapparatus employing magnetics or electromagnetics or magnetic material.In general, hysteresis applies to a lagging or retardation in the valuesof resulting magnetization due to a changing magnetizing force. In manysolenoid actuated devices, this results in a condition wherein theoperation of the device depends not only upon a present state of thedevice, but also upon a prior state.

It is commonly understood that solenoid actuated control valves exhibithysteresis. It is also commonly understood that this hysteresisadversely impacts the consistency of a valve with respect totransitioning between states of no flow and controlled flow in a massflow controller. Nonetheless, in conventional mass flow controllerdesign, this drawback has typically been accepted as a necessarydrawback of using a solenoid actuated control valve, which, for manymanufacturers, is outweighed by the advantages of solenoid actuatedcontrol valve, such as simplicity, cost, and reliability.

SUMMARY OF THE INVENTION

According to one embodiment of the present invention, a method ofconfiguring a mass flow controller for operation with process operatingconditions that differ at least in part from test operating conditionsused during production of the mass flow controller is provided. Themethod comprises acts of establishing a response of the mass flowcontroller with the test operating conditions, and modifying at leastone control parameter of the mass flow controller based on the processoperating conditions such that the response of the mass flow controlleroperating with the process operating conditions does not substantiallychange.

Another embodiment of the present invention includes a computer readablemedium encoded with a program for execution on a processor, the program,when executed on the processor performing a method of configuring a massflow controller for operation with a set of process operating conditionsthat differ at least in part from a set of test operating conditionsused to establish a response of the mass flow controller duringproduction. The method comprises acts of receiving as an input at leastone of process fluid species information and process operatingconditions, and modifying at least one control parameter of the massflow controller based on the input such that the response of the massflow controller does not substantially change when operated with theprocess operating conditions.

According to another embodiment of the present invention a method forconfiguring a mass flow controller having a first response when usedwith a first set of operating conditions and having a second response,substantially different than the first response, when used with a secondset of operating conditions before configuration is provided. The methodcomprises act of operating the mass flow controller with the first setof operating conditions, obtaining configuration data from the mass flowcontroller during the act of operating, setting at least one controlparameter of the mass flow controller based upon the configuration datato provide the first response with the first set of operatingconditions, and modifying at least one control parameter based at leastin part on the configuration data to provide the first response with thesecond set of operating conditions.

According to another embodiment of the present invention a method forconfiguring a mass flow controller having a control loop that includes aflow meter that monitors an actual flow of fluid provided by the massflow controller and provides a conditioned output signal, the flow meterhaving a first gain term, a control section that receives a second inputsignal indicative of a desired flow of the fluid to be provided by themass flow controller and provides a control signal, the control sectionhaving a second gain term that is a function of at least one variableoperating condition, a valve that permits fluid flow based on thedisplacement of one or more elements of the valve, the valve having athird gain term, and a valve actuator that receives the control signaland adjusts the displacement of one or more elements in the valve, thevalve actuator having a fourth gain term to have a substantiallyconstant control loop gain is provided. The method comprises acts ofdetermining the first, third, and fourth gain terms with a first fluidusing a first set of operating conditions, predicting how the first,third, and fourth gain terms will change with at least one of a secondfluid and a second set of operating conditions, and changing the secondgain term to a constant times the reciprocal of the product of thefirst, third and fourth gain terms to provide the substantially constantcontrol loop gain with respect to at least the at least one variableoperating condition.

According to another embodiment of the present invention a method ofcontrolling a mass flow controller having a plurality of componentsdefining a control loop of the mass flow controller is provided. Themethod of comprises acts of forming at least one control loop controlparameter that is a function of at least one variable operatingcondition, and maintaining a constant loop gain of the control loop withrespect to at least the at least one variable operating condition byapplying the at least one control loop control parameter to the controlloop of the mass flow controller.

Another embodiment of the present invention includes a mass flowcontroller comprising a flow meter adapted to sense fluid flow in a flowpath and provide a flow signal indicative of the mass flow rate in theflow path, a controller coupled to the flow meter for providing a drivesignal based at least in part on the flow signal, a valve actuator toreceive the drive signal from the controller, and a valve controlled bythe valve actuator and coupled to fluid path. The mass flow controllerfurther comprises a control loop of the mass flow controller having aconstant closed loop gain.

Another embodiment of the present invention includes a mass flowcontroller having a control loop, the mass flow controller comprising aflow meter adapted to sense fluid flow in a fluid flow path and providea flow signal indicative of the mass flow rate in the flow path, acontroller coupled to the flow meter and adapted to provide a drivesignal based at least in part on the flow signal, a valve actuatoradapted to receive the drive signal from the controller, a valve adaptedto be controlled by the valve actuator and coupled to the fluid flowpath, wherein the control loop of the mass flow controller includes theflow meter, the controller, the valve actuator, and the valve, andwherein the control loop is adapted to have a substantially constantcontrol loop gain term with respect to at least one variable operatingcondition during operation.

According to another embodiment of the present invention, a mass flowcontroller is provided. The mass flow controller comprises a flow meter,having a first gain term, to sense a mass flow rate of a fluid in a flowpath of the mass flow controller and provide a flow signal indicative ofthe mass flow rate of the fluid in the flow path, a valve, having asecond gain term, to receive a control signal that controls the massflow rate of the fluid in the flow path, a valve actuator, having athird gain term, to receive a drive signal and provide the controlsignal to the valve, and a controller. The controller has a first inputto receive the flow signal, a second input to receive a set point signalindicative of a desired mass flow rate of the fluid, and an output thatprovides the drive signal to the valve actuator. The controller isadapted to provide a reciprocal gain term formed by taking a reciprocalof a product of at least one of the first gain term, the second gainterm, and the third gain term.

According to another aspect of the present invention, a method ofdetermining a displacement of a valve having a valve inlet to receive aflow of fluid at an inlet pressure and a valve outlet to provide theflow of fluid at an outlet pressure is provided. The method comprisesacts of selecting an intermediate pressure between the inlet pressureand the outlet pressure, determining a first displacement of the valvebased upon a viscous pressure drop from the inlet pressure to theintermediate pressure, determining a second displacement of the valvebased upon an inviscid pressure drop from the intermediate pressure tothe outlet pressure, determining whether the first displacement isapproximately equal to the second displacement, and selecting one of thefirst displacement and the second displacement as the displacement ofthe valve when the first displacement is approximately equal to thesecond displacement.

According to another aspect of the present invention, a method ofreducing the effects of hysteresis in a solenoid actuated device isprovided. In one embodiment, the method comprises an act of applying apredetermined non-operational signal to the solenoid actuated device toplace the device in a predetermined state.

According to another embodiment, the method of operating the solenoidactuated device, comprises acts of (a) providing a first amount ofenergy to the solenoid actuated device to move the solenoid actuateddevice from a first position to a second position, (b) providing asecond amount of energy to the solenoid actuated device to return thesolenoid actuated device to the first position, and (c) setting thesolenoid actuated device to a predetermined state after the act (b) whenthe first amount of energy exceeds a predetermined amount of energy.

According to another embodiment of the present invention, an apparatusis provided comprising a solenoid actuated device, and a solenoidactuator that is coupled to the solenoid actuated device. The actuatoris adapted to provide a non-operational signal to the solenoid actuateddevice to set the device to a predetermined state.

According to another embodiment of the present invention, a method ofconfiguring a mass flow controller for operation with a set of processoperating conditions that differ at least in part from a set of testoperating conditions used to establish a first response of the mass flowcontroller during production is provided. The method comprises acts ofcharacterizing the mass flow controller with the first set of operatingconditions, obtaining configuration data during the act ofcharacterizing, and modifying at least one control parameter based onthe configuration data and the process operating conditions such thatthe response of the mass flow controller does not substantially change.

According to another aspect of present invention, a spline may be usedto form a linearization curve that linearizes an output signal of a massflow meter. According to one embodiment, a cubic spline may be used todefine a transfer function of the mass flow meter. According to anotherembodiment, a cubic spline may be fitted to an inverse of a transferfunction of the mass flow meter.

Various advantages, novel features, and objects of the invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunction with the accompanying drawings, which areschematic and which are not intended to be drawn to scale. In thefigures, each identical or nearly identical component that isillustrated in various figures is represented by a single numeral. Forpurposes of clarity, not every component is labeled in every figure, noris every component of each embodiment of the invention shown whereillustration is not necessary to allow those of ordinary skill in theart to understand the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 illustrates a schematic block diagram of a mass flow controlleraccording to an embodiment of the present invention that may be usedwith a variety of different fluids and in a variety of differentoperating conditions;

FIG. 2 is a more detailed schematic block diagram of the flow metershown in FIG. 1;

FIG. 3 illustrates various output signals of a mass flow sensor inresponse to a step change in flow according to an embodiment of thepresent invention;

FIG. 4 is a more detailed schematic diagram of the Gain/Lead/Lagcontroller circuit shown in FIG. 1;

FIG. 5 is a more detailed schematic block diagram of the valve actuatorshown in FIG. 1;

FIG. 6 illustrates signal waveforms of a number of the signals shown inFIG. 4;

FIG. 7 a-7 f illustrates a method of configuring a mass flow sensor foroperation with a process fluid and/or process operating conditionsaccording to an embodiment of the present invention;

FIG. 8 illustrates the principle of hysteresis in a normally-closedsolenoid actuated control valve of a mass flow controller according tothe prior art;

FIG. 9 illustrates a diminishing amplitude sinusoidal-shaped signal thatmay be provided to a solenoid actuated control valve to mitigate theeffects of hysteresis according to an embodiment of the presentinvention;

FIG. 10 illustrates a diminishing amplitude square-shaped signal thatmay be provided to a solenoid actuated control valve to mitigate theeffects of hysteresis according to another embodiment of the presentinvention;

FIG. 11 illustrates yet another diminishing amplitude sinusoidal-shapedsignal that may be provided to a solenoid actuated control valve tomitigate the effects of hysteresis according to another embodiment ofthe present invention;

FIG. 12 illustrates a constant amplitude saw-shaped signal that may beprovided to a solenoid actuated control valve to mitigate the effects ofhysteresis according to another embodiment of the present invention;

FIG. 13 illustrates a pulsed signal that may be provided to a solenoidactuated control valve to mitigate the effects of hysteresis accordingto yet another embodiment of the present invention;

FIG. 14 illustrates an embodiment of the present invention including acomputer and a mass flow controller wherein the mass flow controller maybe automatically configured by a computer;

FIG. 15 illustrates an embodiment of the present invention showing amass flow controller that is auto-configurable; and

FIG. 16 illustrates a cross-sectional view of a valve.

DETAILED DESCRIPTION OF THE INVENTION

Mass flow controllers are often vulnerable to instability due to factorsranging from non-linearities in the various components of the mass flowcontroller and/or dependencies on various operating conditions of a massflow controller. The term operating condition applies generally to anyof various conditions that can be controlled and that may influence theoperation of a mass flow controller. In particular, operating conditionsapply to various external conditions that can be controlled independentof a particular mass flow controller. Exemplary operating conditionsinclude, but are not limited to, fluid species, set point or flow rate,inlet and/or outlet pressure, temperature, etc.

However, it should be appreciated that other internal conditions may bepresent during the operation of a mass flow controller such as signalcharacteristics, system noise, or perturbations that cannot becontrolled independent of a particular flow controller. In particular,various signals employed by the mass flow controller may have frequencycomponents containing many different frequencies. However, the frequencycomposition of a signal is inherent to the signal and is not consideredto be controllable independent of a particular mass flow controller.Accordingly, such conditions, unless specifically stated otherwise, arenot considered to be encompassed within the term operating conditions inthis disclosure.

The term mass flow rate, fluid flow, and flow rate will be usedinterchangeably herein to describe the amount of fluid flowing through aunit volume of a flow path (e.g. flow path 103 of FIG. 1), or a portionof the flow path, per unit time (i.e., fluid mass flux).

The term species applies generally to the properties of a specificinstance of a fluid. A change in species may include a change in fluidtype (e.g., from nitrogen to hydrogen), a change in the composition of afluid (e.g., if the fluid is a combination of gases or liquids, etc.),and/or a change in the state of the fluid or combination of fluids. Inparticular, a change in species applies to a change in at least oneproperty of a fluid that may change or affect the performance of a massflow controller. The term species information applies generally to anynumber of properties that define a particular fluid species. Forexample, species information may include, but is not limited to, fluidtype (e.g. hydrogen, nitrogen, etc.), fluid composition (e.g., hydrogenand nitrogen), molecular weight, specific heat, state (e.g., liquid,gas, etc.), viscocity, etc.

Often a mass flow controller will comprise several different components(i.e., a flow sensor, feedback controller, valve etc.) coupled togetherin a control loop. Each component that is part of the control loop mayhave an associated gain. In general, the term gain refers to therelationship between an input and an output of a particular component orgroup of components. For instance, a gain may represent a ratio of achange in output to a change in input. A gain may be a function of oneor more variables, for example, one or more operating conditions and/orcharacteristics of a mass flow controller (e.g., flow rate, inlet and/oroutlet pressure, temperature, valve displacement, etc.) In general, sucha gain function will be referred to as a gain term. A gain term, andmore particularly, the representation of a gain term may be a curve, asample of a function, discrete data points, point pairs, a constant,etc.

Each of the various components or group of components of a mass flowcontroller may have an associated gain term (a component having noappreciable gain term can be considered as having a unity gain term).The relationship between gain terms associated with the variouscomponents of a mass flow controller is often complex. For example, thedifferent gain terms may be functions of different variables (i.e.,operating conditions and/or characteristics of the components), may bein part non-linear, and may be disproportionate with respect to oneanother.

Accordingly, the contributions of each gain term associated with thecomponents around a control loop of a mass flow controller will itselfbe a gain term. This composite gain term may itself be a function of oneor more variables and may contribute, at least in part, to thesensitivity of the mass flow controller with respect to change inoperating conditions and/or characteristics of the various components ofthe mass flow controller.

According to one aspect of the present invention, a mass flow controlleris provided having a control loop with a constant loop gain. Accordingto one embodiment, the constant loop gain is provided by determining areciprocal gain term by forming the reciprocal of the product of thegain terms associated with one or more components around the controlloop of the mass flow controller and applying the reciprocal gain termto the control loop.

A constant loop gain describes a gain of a control loop of a mass flowcontroller that remains substantially constant with respect to one ormore operating conditions of the mass flow controller. In particular, aconstant loop gain does not vary as a function of specific operatingconditions associated with a mass flow controller, or as a function ofthe individual gain terms associated with the control loop. It should beappreciated that a constant loop gain may not be precisely constant.Imprecision in measurements, computation and calculations may cause theconstant loop gain to vary. However, such variation should be consideredencompassed by the definition of a constant loop gain as used herein.

It should further be appreciated that the gain of certain components ofthe mass flow control may vary with operating frequency, and thatsignals of the mass flow controller may have frequency components atmany different frequencies. However, frequency is not considered anoperating condition, and as such, is not considered as a condition overwhich a constant loop gain remains constant.

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, methods and apparatus according to thepresent invention for control and configuration of a mass flowcontroller. It should be appreciated that various aspects of theinvention, as discussed above and outlined further below, may beimplemented in any of numerous ways, as the invention is not limited toany particular implementation. Examples of specific implementation areprovided for illustrative purposes only.

In this description, various aspects and features of the presentinvention will be described. The various aspects and features arediscussed separately for clarity. One skilled in the art will appreciatethat the features may be selectively combined in a mass flow controllerdepending on the particular application.

A. Control of a Mass Flow Controller

FIG. 1 illustrates a schematic block diagram of a mass flow controlleraccording to one embodiment of the present invention. The mass flowcontroller illustrated in FIG. 1 includes a flow meter 110, aGain/Lead/Lag (GLL) controller 150, a valve actuator 160, and a valve170.

The flow meter 110 is coupled to a flow path 103. The flow meter 110senses the flow rate of a fluid in the flow path, or portion of the flowpath, and provides a flow signal FS2 indicative of the sensed flow rate.The flow signal FS2 is provided to a first input of GLL controller 150.

In addition, GLL controller 150 includes a second input to receive a setpoint signal S12. A set point refers to an indication of the desiredfluid flow to be provided by the mass flow controller 100. As shown inFIG. 1, the set point signal S12 may first be passed through a slew ratelimiter or filter 130 prior to being provided to the GLL controller 150.The filter 130 serves to limit instantaneous changes in the set point insignal SI1 from being provided directly to the GLL controller 150, suchthat changes in the flow take place over a specified period of time. Itshould be appreciated that the use of a slew rate limiter or filter 130is not necessary to practice the invention, and may be omitted incertain embodiments of the present invention, and that any of a varietyof signals capable of providing indication of the desired fluid flow isconsidered a suitable set point signal. The term set point, withoutreference to a particular signal, describes a value that represents adesired fluid flow.

Based in part on the flow signal FS2 and the set point signal SI2, theGLL controller 150 provides a drive signal DS to the valve actuator 160that controls the valve 170. The valve 170 is typically positioneddownstream from the flow meter 110 and permits a certain mass flow ratedepending, at least in part, upon the displacement of a controlledportion of the valve. The controlled portion of the valve may be amoveable plunger placed across a cross-section of the flow path, asdescribed in more detail with respect to FIG. 16. The valve controls theflow rate in the fluid path by increasing or decreasing the area of anopening in the cross section where fluid is permitted to flow.Typically, mass flow rate is controlled by mechanically displacing thecontrolled portion of the valve by a desired amount. The termdisplacement is used generally to describe the variable of a valve onwhich mass flow rate is, at least in part, dependent.

The displacement of the valve is often controlled by a valve actuator,such as a solenoid actuator, a piezoelectric actuator, a stepperactuator etc. In FIG. 1, valve actuator 160 is a solenoid type actuator,however, the present invention is not so limited, as other alternativetypes of valve actuators may be used. The valve actuator 160 receivesdrive signal DS from the controller and converts the signal DS into amechanical displacement of the controlled portion of the valve.

As discussed above, the various components of the mass flow controllermay have a gain term associated with the operation thereof. For example,FIG. 1 illustrates gain terms A, B, C and D associated with the flowmeter 110, the GLL controller 150, the valve actuator 160, and valve170, respectively. These components and their associated input andoutput signals, in particular, flow signal FS2, drive signal DS, valvesignal AD, and the fluid flowing in the flow path 103, form a controlloop of the mass flow controller. The gains A, B, C, and D, in turn, areassociated with the relationship between said inputs and outputs. Itshould be appreciated that the gain terms around this control loopcontribute to a composite control loop gain.

Typically, this control loop gain term is the product of the gain termsaround the control loop (i.e., the control loop gain term is equal tothe product A*B*C*D). As used herein, a composite gain term describesany gain term comprising the contributions of a plurality of individualgain terms. The notation for a composite gain term used herein will beappear as the concatenation of the symbols used to represent theindividual gain terms contributing to the composite gain term. Forexample, the control loop gain term describe above will be representedas gain term ABCD. Unless otherwise noted, the notation described abovefor a composite gain term is assumed to be the product of itsconstituent gain terms.

The individual gain terms associated with a control loop of a mass flowcontroller may have differing characteristics and dependencies resultingin a composite gain term that may have multiple dependencies. Thesedependencies or variables may include set point or flow rate, fluidspecies, temperature, inlet and/or outlet pressure, valve displacement,etc. Applicants have recognized and appreciated that a mass flowcontroller having an arbitrary control loop gain term may be vulnerableto instability and may be sensitive to changes in some or all of thedependencies mentioned above. Below is a description of each of theexemplary gain terms illustrated in FIG. 1.

Gain term A is associated with the flow meter and represents therelationship between the actual fluid flow through the mass flowcontroller and the indicated flow (e.g., FS2) of the flow meter (e.g.,change in indicated flow divided by change in actual fluid flow). Gainterm A is calibrated to be a constant function of at least flow rate.However, this constant may depend at least upon the fluid species withwhich the mass flow controller operates.

Gain term B is associated with the GLL controller and represents therelationship between the indicated flow signal FS2 received from theflow meter and the drive signal DS provided to the valve actuator. Gainterm B is related to the various gains and constants used in thefeedback control of the GLL controller.

Gain term C is associated with the valve actuator and represents therelationship between a drive signal and the displacement of the valve.Gain C may include the combination of two separate gains including thegain associated with the conversion of a drive signal to an electricalcurrent or voltage control signal, and the gain associated with thecontrol signal and the mechanical displacement of the controlled portionof the valve.

Gain term D is associated with the valve and represents the relationshipbetween a flow rate of the mass flow controller and valve displacement(e.g., a change in flow rate divided by a change in valve displacement.)Gain term D may be dependent on a variety of operating conditionsincluding fluid species, inlet and outlet pressure, temperature, valvedisplacement, etc. According to one aspect of the present inventiondescribed in more detail below, a physical model of a valve is providedthat facilitates the determination of a gain term associated with thevalve with arbitrary fluids and operating conditions.

Gain term G is a reciprocal gain term formed from the reciprocal of theproduct of gain terms A, C, and D. As will be appreciated further fromthe discussion herein, gain term G permits the mass flow controller tooperate in a consistent manner irrespective of operating conditions byproviding to a control loop of the mass flow controller a constant loopgain.

According to one aspect of the present invention, a system gain term isdetermined for a particular mass flow controller by determining thecomposite gain term of various components around the control loop of themass flow controller. A reciprocal gain term is formed by taking thereciprocal of the system gain term. This reciprocal gain term is thenapplied to the control loop such that the control loop operates with aconstant loop gain. Thus, as the various gain terms around the controlloop vary, the reciprocal gain term may be varied in order to maintain aconstant loop gain.

Because the loop gain of the mass flow controller is held constantirrespective of the type of fluid used with the mass flow controller,and irrespective of the operating conditions with which the mass flowcontroller is operated, the response of the mass flow controller withdifferent fluids and/or operating conditions can be made stable and toexhibit the same behavior as that observed during production of the massflow controller on a test fluid and test operating conditions.

Unless otherwise noted, the system gain term is the composite of gainterms around the control loop associated with various components of themass flow controller that inherently vary as a function of one or moreoperating conditions. For example, the system gain term in FIG. 1 iscomposite gain term ACD.

In block 140 of FIG. 1, a reciprocal gain term G is formed by taking thereciprocal of system gain term ACD and applying it as one of the inputsto the GLL controller. It should be appreciated that the reciprocal gainterm may be the reciprocal of fewer than all of the gain termsassociated with the various components around the control loop of themass flow controller. For example, improvements in control and stabilitymay be achieved by forming the reciprocal of composite gain terms AC,AD, CD etc. However, in preferred embodiments, gain term G is formedsuch that the loop gain remains a constant (i.e., gain G is thereciprocal of the system gain term).

FIG. 2 illustrates a more detailed schematic block diagram of the flowmeter 110. A flow meter refers generally to any of various componentsthat sense flow rate through a flow path, or a portion of a flow path,and provide a signal indicative of the flow rate. The flow meter 110 ofFIG. 2 includes a bypass 210, a sensor and sensor electronics 230, anormalization circuit 240 to receive the sensor signal FS1 from thesensor and sensor electronics 230, a response compensation circuit 250coupled to the normalization circuit 240, and a linearization circuit260 coupled to the response compensation circuit 250. The output oflinearization 260 is the flow signal FS2 as illustrated in the mass flowcontroller of FIG. 1.

Although not shown in FIG. 2, in some embodiments, the sensor signal FS1may be converted to a digital signal with the use of an analog todigital (A/D) converter so that all further signal processing of themass flow controller 100 may be performed by a digital computer ordigital signal processor (DSP). Although in one preferred embodiment,all signal processing performed by the mass flow controller 100 isperformed digitally, the present invention is not so limited, as analogprocessing techniques may alternatively be used.

In FIG. 2, a sensor conduit 220 diverts some portion of the fluidflowing through the flow path, with the remainder and majority of thefluid flowing through the bypass. Sensor and sensor electronics 230 arecoupled to the sensor conduit and measure the flow rate through theconduit. The amount of fluid flowing through the conduit is proportionalto the fluid flowing in the bypass. However, within the range of flowrates with which a mass flow controller is intended to operate, therelationship between the flow rate in the conduit and the flow rate inthe bypass may not be linear.

In addition, thermal sensors measure flow rate by detecting temperaturechanges across an interval of the conduit. Accordingly, in someembodiments, particularly those that implement thermal sensors, theremay exist temperature dependencies, particularly at the two extremes ofthe range of flow rates with which a mass flow controller operates(referred to herein as zero flow and full scale flow, respectively).

Normalization circuit 240 receives the sensor signal FS1 and correctsfor potential temperature dependence at zero flow and at full scaleflow. In particular, when no fluid is flowing through the conduit and/orbypass (i.e., zero flow), the sensor may produce a non-zero sensorsignal. Furthermore, this spurious indication of flow may depend ontemperature. Similarly, the sensor signal FS1 may experience fluctuationthat is dependent on temperature at full-scale flow. Correction fortemperature dependent variation in the signal FS1 at zero flow may beperformed by measuring the value of the sensor signal FS1 at zero flowat a number of different temperatures, and then applying a correctionfactor to the signal FS1 based upon the temperature of the sensor.Corrections for temperature dependent variation of sensor signal FS1 atfull-scale flow may be performed in a similar manner based uponmeasurements of the sensor signal at different values of temperature andapplying an appropriate correction factor based on the temperature.

In addition, temperature dependencies may be similarly measured forcharacteristic points along the entire range at which a mass flowcontroller is desired to operate. Accordingly, a correction curve thatis a function of flow rate and temperature may be fit to themeasurements taken a zero flow, full scale flow, and any number ofcharacteristic points in between. This correction curve may providecorrection for temperature dependencies across the range of flow ratewith which the mass flow controller is intended to operate. In addition,a knowledge of the fluid being used and known sensor property variationswith temperature may be utilized to provide or enhance the correctionfactors and/or correction curves of normalization 240.

The normalization circuit 240 may also provide a fixed normalizationgain to the signal FS1 so that at full scale flow through the sensorconduit, a specific value is obtained for normalization signal FS1′, andat zero flow, another specific value (e.g. zero) is obtained.

In one embodiment, for example, normalization 240 ensures that at zeroflow through the sensor conduit, normalization signal FS1′ has a valueof 0.0, and at full scale flow through the conduit, normalization signalFS1′ has a value of 1.0. It should be appreciated that any value may bechosen for normalization signal FS1′ at zero flow and at full scaleflow, as values used herein are exemplary only.

It should be appreciated that normalization signal FS1′ may have poordynamic characteristics, such that in response to a step change in fluidflow, the signal FS1′ is delayed in time and smoothed relative to theactual flow through the flow sensor. This is because thermal flowsensors typically have a slow response time as the thermal changes takeplace over a relatively long period of time.

FIG. 3 is an illustration of this behavior in which time is plotted onthe horizontal or X-axis and flow is plotted on the vertical or Y-axis.As shown in FIG. 3, in response to a unit step change in actual flowthrough the thermal mass flow sensor, the signal FS1 provided by thesensor is delayed in time and smoothed.

In order to correct for these sensor effects and provide better dynamicresponse to changes in fluid flow, normalization signal FS1′ is providedto response compensation circuit 250. The response compensation circuit250 is functionally a filter that is approximately an inverse of thetransfer function of the sensor and sensor electronics 230. The responsecompensation circuit 250 may be adjusted or tuned so that theconditioned signal FS1″ provided by the response compensation circuit250 has a predetermined rise time, has a predetermined maximum level ofovershoot and/or undershoot, and levels out within a predetermined timeframe, and/or is tuned for other characteristics that may be desirablefor a particular implementation of a mass flow controller.

As shown in FIG. 3, the compensated signal FS1″ has a profile that moreclosely reflects the profile of the step change in fluid flow throughthe sensor illustrated in the drawing. The flow meter of the mass flowcontroller may be adjusted to provide such a compensated signal duringproduction of the mass flow controller. In particular, the dynamicresponse may be tuned during a sensor tuning step discussed in detailfurther below.

As discussed briefly above, the proportion of fluid flowing through thesensor conduit relative to the fluid flowing through the bypass may bedependent upon the flow rate of the fluid. In addition, non-linearitiesin the sensor and sensor electronics further complicate the relationshipbetween actual fluid flow and the sensed flow signal provided by thesensor at different flow rates. The result is that a curve representingsensed flow versus fluid flow may not be linear.

It should be appreciated that many of these non-linearities carrythrough normalization 240 and response compensation 250. Accordingly,the immediate discussion is germane to any of sensor signals FS1, FS1′,and FS1″. The term sensor output will be used herein to describe thesensor signal before it has been linearized (i.e., precedinglinearization 260.) In particular, and unless otherwise indicated,sensor output describes the signal produced by the sensor and that hasbeen normalized and compensated (e.g., FS1″), for example, bynormalization 240 and response compensation 250, respectively, but thathas not been linearized. It should also be appreciated thatnormalization and compensation steps need not respect the order in whichthey are applied in FIG. 2, and are in fact interchangeable.

Linearization 260 corrects for the non-linearities of the sensor output(i.e., FS1″). For example, linearization 260 provides a flow signal thatwill have a value of 0 at zero flow, 0.25 at 25% of full scale flow, 0.5at 50% of full scale flow, 1.0 at full scale flow etc. Linearization 260provides the flow signal FS2 provided to an input of GLL controller 150as illustrated in FIG. 1. The term indicated flow will be used herein todescribe generally the flow signal provided by a flow meter after it hasbeen linearized (e.g. flow signal FS2).

Although there are a myriad of ways to linearize the sensor output, suchas polynomial linearization, piece-wise linear approximation, etc., inone embodiment of the present invention, a spline is used to linearizethis signal, and in particular, a cubic spline. A discussion of cubicsplines is given in Silverman B. W. entitled “Some Aspects of the SplineSmoothing Approach to Non-Parametric regression Curve Fitting”,published in the Journal of the Royal Statistics Society and is hereinincorporated by reference in its entirety.

According to this aspect of the present invention, the actual outputsignal FS1 from the sensor and sensor electronics 230 is measured at anumber of different (and known) flow rates on a test fluid or gas, andthe measured flow rate is plotted against the known flow rate for allmeasurement points. This plotting of the measured flow rate versus theknown flow rate defines the transfer function of the sensor and sensorelectronics 230, and a cubic spline is then fit to the inverse of thetransfer function of the sensor and sensor electronics 230. The measuredvalue of the sensor output is then used as an input to the cubic splineto provide a normalized, compensated, and linearized indicated flowsignal (e.g., FS2).

As will be discussed in further detail below, the linearization circuit260 may include a linearization table (not shown) to facilitatelinearization of the sensor output. In an alternative embodiment of thepresent invention, a cubic spline is fit to the transfer function of thesensor and sensor electronics 230 itself, rather than its inverse.

After compensating for non-linearities in the sensor and sensorelectronics 230, and for the changing fraction of fluid flow that goesthrough the sensor conduit 220, the conditioned flow signal FS2 isprovided to the GLL controller 150 and may also be provided to a filter120 (FIG. 1) for display. An illustration of the conditioned flow signalFS2 is referenced “conditioned sensed flow (FS2)” and shown in FIG. 3.

As shown in FIG. 1, a gain term A is associated with the flow meter 110.This gain term represents the relationship between the fluid flowing inthe flow path 103 and the indicated flow (i.e., flow signal FS2). Inparticular, gain term A is the ratio of change in indicated flow tochange in actual fluid flow. It should be appreciated from thediscussion of the flow meter 110 above, that this relationship (i.e., acurve of fluid flow versus indicated flow) has been made to be linear.Thus, the ratio of change in indicated flow to change in to actual fluidflow (i.e, the derivative of the curve of fluid flow versus indicatedflow) is a constant function of flow rate. Thus, gain term A is aconstant for a particular fluid species.

Since gain A is a constant, and since indicated flow has been defined ata particular value at full scale flow, gain A can be determined for aparticular fluid based upon the full scale flow associated with thefluid used during production of the mass flow controller. In theexemplary flow meter where indicated flow has been adjusted to have avalue of 1.0 at full scale flow, gain A is simply the reciprocal of fullscale flow.

It should be appreciated that full scale flow through a mass flowcontroller may change as a result of operating the mass flow controllerwith a different fluid. Hence, the mass flow controller will have a fullscale range dependent on fluid species. Therefore, though gain A is aconstant function of at least flow rate, this constant may change uponoperation of the mass flow controller with a different fluid species.

However, Applicants have determined how the gain associated with theflow meter (e.g., gain term A) changes with fluid species. As discussedabove, the gain of the flow meter can be directly calculated from fullscale range (i.e., the full scale flow of the mass flow controller).Thus, determining the full scale range for a process fluid allows for adirect determination of the gain of the flow meter. The full scale rangeof a process fluid may be determined by applying a conversion factor tothe full scale range associated with a test fluid. The conversion factormay be derived empirically from measurements with the particular fluidfor which the full scale range is being determined.

FIG. 4 illustrates details of one embodiment of the GLL controller 150.Although controller 150 is described herein as being a gain/lead/lag(GLL) controller, it should be appreciated that the present invention isnot so limited. For example, the various aspects of the presentinvention may be used with other types of feedback controllers, such asproportional integral differential (PID) controllers, proportionalintegral (PI) controllers, integral differential (ID) controllers, etc.It should also be appreciated that numerous mathematical equivalents tothe GLL controller 150 illustrated in FIG. 4 may alternatively be used,as the present invention is not limited to the specific controllerstructure illustrated therein.

The GLL controller 150 receives three input signals: the flow signal FS2(also referred to as indicated flow); the set point signal SI2; and thereciprocal gain term G. As noted above, the set point signal SI2 mayfirst be passed through a slew-rate limiter or filter 130 to preventinstantaneous changes in the set point signal from being provided to theGLL controller.

As noted in the foregoing, the Gain G 140 is a reciprocal gain termformed by taking the reciprocal of the product of the gain termsassociated with various components around a control loop of the massflow controller (i.e., the reciprocal of the system gain term), asdiscussed in detail herein. Gain G may be applied anywhere along thecontrol loop and is not limited to being applied at the input of thecontroller of a mass flow controller. However, reciprocal gain term Gmay be conveniently applied to the input of the GLL controller asillustrated in FIGS. 1 and 4.

According to one embodiment of the present invention, gain term G may bedetermined by a microprocessor or digital signal processor associatedwith the mass flow controller. The processor may be integrated into themass flow controller or may be external, as discussed below.

As shown in FIG. 4, the flow signal FS2 is provided to a differentiatoror D-term circuit 410. Because the circuit 410 is not identically adifferentiator, it is referred to as a “D-term” circuit herein. Indeed,within the D-term circuit 410, the flow signal FS2 is differentiated,low pass filtered, and multiplied by a constant and then summed with theconditioned flow signal FS2. It should be appreciated that the presentinvention is not limited to the particular implementation of the D-termcircuit 410 described herein, as other types of differentiator circuitsmay be used. Functionally, the D term circuit 410 provides a modifiedflow signal FS3 that is “sped up” relative to the conditioned signalFS2, thereby constituting the “lead” in the GLL controller 150. The Dterm circuit 410 also provides damping. As should be appreciated bythose skilled in the art, the D-term circuit 410 functionally provides amodified flow signal FS3 that is indicative of how the flow signal ischanging and how quickly.

The modified flow signal FS3 is then provided, along with the set pointsignal SI2 to a subtraction circuit 420 that takes the modified flowsignal FS3 and the set point signal SI2, and generates an error signal Ebased upon their difference. The error signal E is then multiplied bythe gain term G (hence the word “gain” in a gain/lag/lead GLLcontroller) and provided to a proportional gain term 440 and an integralgain term 450.

The proportional gain term multiplies the signal EG by a fixed constantK_(P), and then provides the output signal EGK_(P) to a summing circuit470. The proportional gain term 440 is used to functionally provide acomponent of the drive signal to move the control valve 170 a certainfixed amount based upon the signal EG, thereby allowing the controlvalve 170 to make up ground quickly upon a change in the error signal E.

The proportional gain term 440 also provides damping, helping to preventringing in the drive signal DS and in the resulting flow. For example,as the error signal E decreases, and the output signal from theintegrator 460 is increasing, the value of the error signal E multipliedby K_(P) decreases, as the constant K_(P) is preferably less than unity,thereby decreasing the amount of overshoot that occurs.

The integral gain term 450 multiplies the signal EG by another fixedconstant K_(I), and then provides the output signal EGK_(i) to an inputof the integrator 460. The integrator 460 integrates the signal EGK_(i)and provides the integrated output to a second input of the summingcircuit 470. Functionally, the output of the integrator 460 provides asignal that is indicative of the error signal E over time, andrepresents how the error signal has changed in the past (hence the word“lag” in a gain/lead/lag GLL controller). Given an error signal E, theintegrator 460 starts out at a specific slope, and as the indicated flow(e.g., FS2) increases (assuming a new and higher set point has beeninput), the error signal E decreases, such that the integrator 460 stopsintegrating, (i.e., slows down how fast it's changing) and the componentof the drive signal output from the integrator 460 stops increasing. Theintegrated output signal EGK_(I) is then summed with the output of theproportional gain term EGK_(P) in summing circuit 470, and the summedoutput signal DS is provided as a drive signal to the valve actuator160.

In addition, a pedestal (not shown) may be provided to preset theintegrator 460 to a particular value when the controller istransitioning from a zero flow to a controlled flow state. The pedestaldescribes a value that when added to the integrator will provide a drivelevel DS that is just below the drive level necessary to open the valveand permit flow. In this manner, the time that would have been necessaryfor the integrator to ramp up to the pedestal value can be eliminatedand the controller will have an increased response time to transitionsbetween zero flow and controlled flow.

As shown in FIG. 5, the output of the summing circuit is provided to thevalve actuator 160 which generally includes a valve drive electronicscircuit 510 that is coupled to an electro-mechanical actuator 520. Anysuitable valve drive electronics circuit 510 may be used to receive thedrive signal DS and convert the drive signal DS to a voltage, current,or other signal capable of moving the valve 170 to a desired position togive the desired rate of flow. Further, the valve drive circuit 510 mayinclude any suitable valve drive actuation circuit known in the art fordriving solenoid actuated control valves, piezoelectrically actuatedcontrol valves, etc. According to one embodiment of the presentinvention utilizing a solenoid actuated control valve, the valve driveelectronics circuit 510 may include circuitry that reduces the impact ofhysteresis in the solenoid actuated control valve as described furtherin detail below.

FIG. 6 is an illustration of a number of the signals described abovewith respect to FIG. 4 in which the horizontal or X-axis represents timeand the vertical or Y-axis represents the identified signal level. Asshown in FIG. 6A, at a time T₀, a step change (to the level F₀) in theset point in signal SI2 is provided. At this time, the error signal Erises to the level F₀, as the error signal E is equal to the differencebetween the conditioned flow signal FS2 (which is still at its priorstate), and the value of the set point in signal SI2, which is now at avalue of F₀. The error signal times the gain term G (i.e., signal EG)thus steps to a high value and then decreases with time in the mannershown in FIG. 6B. As the output of the proportional gain term 440 is thesignal EG multiplied by the constant K_(P) (which is less than unity),the signal EGK_(P) has a similar shape, although slightly reduced inamplitude, as shown in FIG. 6C. As shown in FIG. 6D, at the time T₀, theintegrated output signal EGK_(I) is zero, but quickly starts rampingupward due to the magnitude of the error signal E. The output of thesumming circuit 470, representing the sum of the output signal EGK_(P)and the integrated output signal EGK_(I) is labeled DS and is shown inFIG. 6E. Based upon the drive signal DS provided to the valve drive andvalve drive electronics circuit 160, the control valve 170 is opened anincreased amount and the indicated flow signal (e.g., flow signal FS2)starts increasing to the new level of the set point in SI2. As timeprogresses, the error signal E decreases, the output signal EGK_(P) ofthe proportional gain term 440 decreases, as does the integrated outputsignal EGK_(I), and the rate of flow is established at the level of thenew set point.

Ideally, it is desired to get a step response in the true flow inresponse to a step input applied to the set point in of the mass flowcontroller. Although this is not practically possible, embodiments ofthe present invention may be used to provide a consistent response inresponse to a step input in the set point, irrespective of whether thestep input represents a 2% step or a 100% step relative to full scaleflow, irrespective of the fluid being used, and irrespective of theinlet or outlet pressure, etc. To obtain this consistency, embodimentsof the present invention provide a mass flow controller having aconstant loop gain.

It should be appreciated from the foregoing that while various gainsassociated with the components along a control loop of a mass flowcontroller may vary as functions of different variables, and may dependupon a variety of different operating conditions, consistent and stableoperation of a mass flow controller can be attained for a set ofoperating conditions by providing the control loop of the mass flowcontroller with a constant loop gain.

It should be appreciated that various aspects of the control of a massflow controller may be implemented using a microprocessor. For example,GLL controller 150 may be implemented as a microprocessor, digitalsignal processor etc. Likewise, the determination of various controlparameters such as the reciprocal gain term (e.g., gain term G) may beprovided by a microprocessor. Various aspects of the control of a massflow controller may be implemented in software, firmware or hardwareusing techniques that are well known in the art.

B. Mass Flow Controller Configuration

It should be appreciated that in many cases, in order for a mass flowcontroller to operate consistently and in a stable manner, the mass flowcontroller must be tuned and/or calibrated during production. Manualtuning and/or calibration is often a time consuming, labor intensive,and expensive process. In addition, when a process requires that themass flow controller be configured to operate with a different fluidspecies and/or operating conditions than that used during production,the performance of a mass flow controller will rarely exhibit the samebehavior observed during production of the mass flow controller, even ifthe mass flow controller was tuned and calibrated on a number of processfluids. In other words, the mass flow controller may have a differentresponse when operating with a fluid and/or operating conditions otherthan that with which the mass flow controller was tuned and/orcalibrated.

According to one aspect of the present invention, a method ofconfiguring a mass flow controller is provided that permits the responseof the mass flow with a process fluid and/or process operatingconditions to be made substantially the same as the response for whichthe mass flow controller was tuned and/or calibrated with a test fluidand test operating conditions.

In one embodiment of the present invention, during tuning and/orcalibration of a mass flow controller with a single test fluid and a setof test operating conditions, configuration data is obtained. Thisconfiguration data may be used to configure the mass flow controller tooperate with an arbitrary process fluid and/or operating conditions,thus alleviating performance degradation due to operation with a fluidand/or operating conditions other than those used during production, andobviating expensive and time-consuming tuning and/or calibration of themass flow controller on multiple surrogate fluids.

Providing a mass flow controller that is capable of operating witharbitrary fluids and operating conditions and exhibiting a satisfactoryresponse often involves steps including an initial production of themass flow controller and a subsequent configuration of the mass flowcontroller. FIG. 7 a illustrates production and configuration stepsaccording to one embodiment of the present invention.

The term production, as used herein and when applied to a mass flowcontroller, describes generally the various tasks involved in preparinga mass flow controller for operation on a specific fluid species and aparticular set of operating conditions. Production may include buildingthe mass flow controller from various components, operating the massflow controller on a test fluid under test operating conditions, andtuning and/or calibrating various components and/or control parametersof the mass flow controller such that the mass flow controller exhibitssatisfactory behavior and performance (i.e., has a satisfactoryresponse) with the test fluid and test operating conditions.

The term configuration or configuring, as used herein and when appliedto a mass flow controller, describes generally the various stepsinvolved in adapting a mass flow controller for operation with anarbitrary fluid under arbitrary operating conditions. In particular,configuration describes steps involved in adapting a mass flowcontroller for operation with a fluid other than the fluid with whichthe mass flow controller underwent production (referred to herein as a“process fluid” and a “test fluid”, respectively), and under conditionsthat may be different than the set of operating conditions used duringproduction of the mass flow controller (referred to herein as “processoperating conditions” and “test operating conditions”, respectively),such that the response of the mass flow controller is substantially thesame as that observed during production. It should be appreciated thatconfiguration of a mass flow controller may be performed at any timeafter production, and in any location, including, but not limited to,the manufacturing site (e.g., to configure the mass flow controller fora particular known application), or the field (e.g., at an end user'ssite of operation).

In general, the term satisfactory response refers to a response of amass flow controller that performs within a set of given tolerances of aparticular mass flow control process or task. In particular, the dynamicand static response of the mass flow controller performs within a rangeof tolerances for which the mass flow controller was intended tooperate.

A mass flow controller may be tuned and/or calibrated during productionto have a satisfactory response for an arbitrary set of tolerances.Thus, the response of a mass flow controller after tuning and/orcalibration on a test fluid and a set of test operating conditions,unless otherwise stated, should be considered to have a satisfactoryresponse for that test fluid and operating conditions. However, theresponse may change substantially when the mass flow controller isoperated with a different fluid and/or operating conditions, such thatthe response is no longer satisfactory.

In general, a mass flow controller is considered to have the sameresponse on a test fluid and test operating conditions and on a processfluid and/or process operating conditions when both responses aresatisfactory (i.e., both responses perform within the tolerances forwhich the mass flow controller was intended to operate).

As illustrated in FIG. 7 a, during production 710, the mass flowcontroller is operated with a test fluid under a set of test operatingconditions. Characteristics of the operation of the mass flow controllerare obtained and stored as configuration data 712. The configurationdata 712 may be obtained during various tuning and/or calibration stepsof production 710, as described in further detail with respect to FIGS.7 b-7 f.

The term tuning describes steps that involve providing satisfactorydynamic response and behavior to fluid flow and a change in fluid flowand/or change in desired fluid flow (i.e., a change in set point). Theterm calibration refers generally to steps that involve providing asatisfactory steady-state or static response of a mass flow controller.

The term configuration data applies generally to information obtainedduring tuning and/or calibration of a mass flow controller. Inparticular, configuration data describes characteristics of and/ormeasurements taken from a mass flow controller during operation with atest fluid and test operating conditions. Configuration data obtainedduring production of a mass flow controller may then be used toconfigure the mass flow controller on a process fluid and/or processoperating conditions.

As discussed briefly above, the terms test fluid and test operatingconditions are used to describe a fluid and operating conditions thatwere used during production of a mass flow controller. The terms processfluid and process operating conditions describe fluids and operatingconditions desired, typically, by an end user for a particularapplication of the mass flow controller.

It should be appreciated that the same type or types of fluids andoperating conditions may be used for both test and process purposes.However, because a mass flow controller cannot be tuned on every fluidand/or under all operating conditions, certain aspects of the inventioninvolve a mass flow controller being tuned and/or calibrated on aparticular test fluid and under a particular set of test operatingconditions during production such that the mass flow controller can beconfigured to operate with a different fluid and/or operating conditionsthereafter. Accordingly, it should be understood that the term “processfluid” is not used to describe different types of fluids, but rather todemonstrate that the fluid may differ from the fluid with which the massflow controller was tuned and/or calibrated. Similarly, the term“process operating conditions” describe a set of operating conditionsthat may not be the same as the test operating conditions with which themass flow controller was tuned and/or calibrated. One, some, or all of aset of process operating conditions may differ from the test operatingconditions.

In configuration step 720, the configuration data 712 obtained duringproduction may be used to facilitate configuration of the mass flowcontroller on a process fluid and/or process operating conditions.According to one embodiment, configuration data 712 is used duringconfiguration 720 to determine control parameters associated with themass flow controller that enable operation of the mass flow controllerwith a process fluid and/or process operating conditions. In particular,the configuration data 712 obtained during a production step 710 is usedto determine control parameters that facilitate the configuration of themass flow controller with a process fluid and process operatingconditions, such that the mass flow controller exhibits a satisfactoryresponse (i.e., the mass flow controller is configured to havesubstantially the same response with the process fluid and/or processoperating conditions as that observed during production using the testfluid and test operating conditions).

The term control parameter as used herein refers generally to parametersassociated with the mass flow controller that facilitate the operationof the mass flow controller. Control parameters may include, but are notlimited to, filter coefficients, gain terms, controller constants,linearization curves etc. In particular, control parameters refer toparameters that may need change, modification, or addition when a massflow controller is configured for operation with an arbitrary processfluid and/or process operating conditions (i.e., configured to exhibit asatisfactory response).

As used herein, the phrase “configured for operation” is intended todescribe configuring a mass flow controller in such a way that whenoperated, the mass flow controller exhibits a satisfactory response(i.e., mass flow controllers having unsatisfactory responses are notgenerally considered operational).

It should be appreciated that, in general, production 710 need only bedone once and with a single test fluid and a set of test operatingconditions. However, configuration 720 may be repeated any number oftimes during the lifetime of a mass flow controller. In particular,whenever it is desirable to operate the mass flow controller with adifferent process fluid and/or operating conditions, it may be desirableto repeat configuration 720 with the new process fluid and/or processoperating conditions such that the mass flow controller exhibits asatisfactory response with the new process fluid and/or processoperating conditions.

It should be further appreciated that production and configuration ofdifferent types of mass flow controllers and different mass flowcontroller implementations may require different steps. However,production should include steps such that the mass flow controller hasbeen properly characterized and a satisfactory response established foroperation with a set of test operating conditions, and that sufficientconfiguration data has been obtained to facilitate subsequentconfiguration of the mass flow controller. Likewise, configuration ingeneral should include steps necessary to establish substantially thesame response when operating with a set of process operating conditionsas that observed during production.

FIG. 7 b illustrates a block diagram according to one embodiment thatincludes various steps that may be performed during the production andthe configuration (e.g. steps 710 and 720 in FIG. 7 a) of a mass flowcontroller. Production 710 may include a sensor tuning step 10, a valvecharacterization step 20, a feedback controller tuning step 30, and acalibration step 40. It should be appreciated that production 710 mayinclude other steps that are not shown in production 710, for example,steps involved with building the mass flow controller, such as bypassmatching etc., that are known in the art.

In the various exemplary steps 10-40 of production 710, the mass flowcontroller is characterized and a satisfactory response is establishedon a set of test operating conditions. Configuration data is obtainedduring production that facilitates configuration of the mass flowcontroller for operation with a set of process operating conditions, asdescribe further in detail below.

In sensor tuning step 10, the flow meter of a mass flow controller istuned such that it exhibits a satisfactory dynamic response. Inparticular, the various components of the flow meter are tuned such thatthe sensor output (e.g. FS1″) responds satisfactorily to changes in flowthrough the sensor. For example, as discussed in connection with FIG. 2,sensor tuning may include providing normalization and responsecompensation filter coefficients, correction curves, and/or gains suchthat the flow meter responds to fluid steps with a sensor output havinga step shape that closely resembles the step changes in fluid flow inthe flow path. Information obtained during tuning step 10, such asfilter coefficients, correction curves and/or gain terms may be storedas configuration data 712.

In valve characterization step 20, the mass flow controller ischaracterized sufficiently such that it can be configured to operate ina consistent and stable manner in response to changes in variousoperating conditions and/or characteristics. According to oneembodiment, a system gain term of a control loop of the mass flowcontroller may be determined and a reciprocal of the system gain termdetermined and applied to the control loop to provide a constant loopgain. In addition, measurements made during the determination of thesystem gain term may be stored as configuration data and later usedduring configuration, as discussed further in detail below with respectto FIG. 7 c.

In feedback controller tuning step 30, the control and controlelectronics associated with the feedback controller are tuned such thatthe mass flow controller exhibits satisfactory dynamic response tochanges in set point. According to one embodiment, the various PIDparameters discussed in connection with FIG. 4 may be set such that theGLL controller exhibits desirable dynamic characteristics such assettling time, maximum overshoot and undershoot, etc.

In calibration step 40, the mass flow controller is calibrated such thatit exhibits satisfactory steady-state response. According to oneembodiment, the mass flow controller is calibrated to provide a linearrelationship between the actual fluid flow through the mass flowcontroller and the flow indicated by the flow meter (e.g. flow signalFS2, also called indicated flow) across the range of flow rates withwhich the mass flow controller was intended to operate.

In the exemplary steps 50 and 60 illustrated in configuration 720, theconfiguration data obtained during production 710 and information aboutthe process operating conditions with which the mass flow controller isto be configured for operation is used to modify control parameters ofthe mass flow controller such that the response established duringproduction does not substantially change when operating the mass flowcontroller with the process operating conditions.

As illustrated in FIG. 7 b, configuration 720 of the mass flowcontroller may include a system gain decomposition step 50, and a systemconfiguration step 60. In the system gain decomposition step 50, asystem gain term is obtained and then decomposed into its constituentgain terms based, at least in part, on the configuration data obtainedduring production 710 of the mass flow controller.

However, system gain decomposition step 50 may not be necessary in someimplementations of a mass flow controller and represents only one methodby which a model of actuator behavior may be provided to systemconfiguration step 60.

Accordingly, it should be appreciated that in the examples discussedherein, steps involving measurement and subsequent decomposition of asystem gain term may be unnecessary under circumstances where gain termsassociated with various components of a mass flow controller can beobtained directly. For example, in some mass flow controllers, a stepperactuator may be employed from which the associated gain term may bedirectly obtained from the mechanical design of the actuator. In such acase, measurement of a system gain during production (e.g. recordingCDA′ during valve characterization step 20 in FIG. 7 c) anddecomposition of the system gain term during configuration (e.g. step50) can be omitted since the information provided by decomposing thesystem gain term (e.g., gain term C) can be obtained directly from theactuator itself.

The method of obtaining system gain term information during productionand decomposing the system gain term during configuration, however,provides a method for configuring a mass flow controller that, ingeneral, may be applied to any implementation of a mass flow controllerto provide, for instance, a model of the actuator, where no other may beavailable, or such information cannot be directly obtained. As such,details of this method have been incorporated into production andconfiguration steps described in the embodiments illustrated in FIGS. 7c-7 f. However, aspects of the invention are not limited to using thismethod, nor is it limited to mass flow controllers where this method maybe necessary.

In the system configuration step 60, control parameters are determinedfor a process fluid and/or process operating conditions for which themass flow controller is being configured, such that the mass flowcontroller exhibits a satisfactory response when operating with theprocess fluid and/or process operating conditions. According to oneembodiment, a reciprocal gain term may be formed from the reciprocal ofthe product of the individual gain terms associated with variouscomponents of the mass flow controller operating with the processoperating conditions. The gain terms may be determined from a physicalmodel of the valve and the valve actuator. The reciprocal gain term maybe applied to a control loop of the mass flow controller to provide aconstant loop gain.

Further details of exemplary production steps and configuration stepsare now described in connection with FIGS. 7 c-7 f.

FIGS. 7 c and 7 d illustrate one exemplary procedure for obtainingconfiguration data during tuning and/or calibration of a mass flowcontroller during production.

FIGS. 7 e and 7 f illustrate another exemplary procedure for configuringthe mass flow controller to operate on a process fluid and/or processoperating conditions different from those with which the mass flowcontroller was tuned and/or calibrated.

The procedures for production and configuration illustrated in FIGS. 7c-7 f may be applied to a mass flow controller similar to thatillustrated in FIG. 1. However, it should be appreciated that theseaspects of the present invention are not so limited, and may be appliedto a variety of mass flow controllers having a variety of differentcomponents and operating characteristics.

In FIGS. 7 c-7 f, exemplary information that may be stored asconfiguration data during the production of a mass flow controller areillustrated under the heading “Configuration Data” and placed withinblocks labeled 712. It should be appreciated that the informationillustrated in the drawings is not limiting, nor should it be considereda requirement. Each implementation of a mass flow controller may have adifferent set of configuration data that facilitates the configurationof the mass flow controller for operation with a process fluid and/orprocess operating conditions.

FIG. 7 c illustrates further details of a sensor tuning step 10 and avalve characterization step 20 according to one embodiment of thepresent invention. In sensor tuning step 10, the flow meter of a massflow controller is tuned such that it exhibits satisfactory dynamicresponse, for example, to a fluid step. A fluid step refers to a changein fluid flow having the characteristics of a step function, includingboth positive and negative steps in fluid flow.

In step 12, fluid steps are applied to the flow sensor. The flow sensoris then tuned in step 14, such that in response to a fluid step, astep-shaped flow signal is provided. Desirable characteristics of thisstep-shaped flow signal may include rise time, settling time, maximumovershoot and undershoot, etc. For example, referring back to the massflow controller described with respect to FIGS. 1 and 2, the step oftuning the flow sensor may include tuning of sensor and sensorelectronics 230, normalization 240, and response compensation 250. Forexample, the filter coefficients of the response compensation filter 250may be tuned to reshape the signal as shown in FIG. 3. It should beappreciated that in general, each implementation of a mass flowcontroller may have a different set of parameters that may be tuned.However, the intent of the sensor tuning process 10 is to ensure thatthe flow sensor exhibits satisfactory dynamic characteristics. As shownin FIG. 7 c, the normalization gain associated with providing a sensoroutput of 1.0 for full scale flow through the sensor conduit may berecorded as configuration data.

In the valve characterization process 20, a test fluid is provided tothe mass flow controller at different set points of a set of selectedset points at a known inlet and outlet pressure. At each set point theresulting drive level is recorded. The term drive level describes thevalue of the drive signal provided to the valve actuator. For instance,the drive level may be the measured value of an electrical current or avoltage potential. The drive level may also be the value of a digitalcontrol signal that may be converted into an electrical signal tocontrol the mechanical displacement of the valve. Signal DS in FIG. 1 isan example of a drive signal, the value of which is the drive level.

In one embodiment, a GLL controller that has not been tuned, but that isknown to converge, is used during this step. Accordingly, each set pointin the set of selected set points will converge to the sensor output. Insome embodiments, the sensor output and drive level information recordedduring this step is used to calculate a composite gain term of the massflow controller. For example, in valve characterization step 20 of FIG.7 c, a composite gain term CDA′ corresponding to the product of the gainterms associated with the valve actuator 160, the valve 170, and theflow meter 110 is calculated from information obtained during thecharacterization of the valve.

In step 21, a series of set points from a selected set of set points isprovided to the mass flow controller. The set of selected set points maybe chosen in any suitable manner. For example, in one embodiment, theset of selected set points are various fractions of full-scale flow thataccount, at some level, for the range with which the mass flowcontroller is intended to operate. The selected set points need not beevenly spaced out across the range of values. In addition, any number ofset points may be selected. In general, the number of set pointsselected should be sufficient to adequately characterize the valveactuator over the range with which the mass flow controller was intendedto operate.

Each of the various selected sets of set points illustrated in FIGS. 7c-7 f need not be identical to one another. In order to illustrate thatthe set points need not be the same in each set, the subscripts vt, cb,and cf, for example, have been used to indicate set points chosen forthe valve characterization, calibration, and configuration steps,respectively. However, it should be appreciated that these sets may bein part or entirely the same.

In step 21, a first set point _(vt)S₀ is chosen from a selected set ofset points {_(vt)S₀, _(vt)S₁, _(vt)S₂, . . . }. A small deviation n ischosen as an offset to the set points _(vt)S_(i). Then, _(vt)S₀+n isapplied to the controller and the controller is allowed to converge.When the controller converges, sensor output will equal the applied setpoint. In step 22, the resulting drive level is recorded for set point_(vt)S_(i).

In step 23, _(vt)S₀−n is applied to the controller and allowed toconverge. The resulting drive level is again recorded as shown in step24. In step 25, a composite gain term CDA′ is determined. For example,the composite gain term may be determined by taking a change in the twoset points (i.e., 2n) and dividing the change by a change in the drivelevels recorded in steps 22 and 24. This ratio represents the compositegain term CDA′ for set point _(vt)S₀. Gain terms C and D, as describedin the foregoing, are associated with the valve actuator and valverespectively. Gain term A′ is associated with the flow meter andrepresents the gain of the flow meter without the contribution oflinearization 260 (i.e., the gain associated with sensor output). Thesensor output value to which the mass flow controller converged for eachset point _(vt)S_(I), and the composite gain term CDA′ determined atthat set point may be stored as configuration data.

Steps 21-25 are repeated for each of the set points _(vt)S_(i) in theset of selected set points. The result is a set of point pairs {sensoroutput, CDA′}_(i). In one embodiment, the set of point pairs {sensoroutput, CDA′}_(i) is recorded as configuration data for the manualtuning of the mass flow controller. In addition, for each CDA′ recordedin step 20, a reciprocal gain term G=1/CDA′ may be formed. Thisreciprocal gain term G may be provided to the controller in thesucceeding controller tuning step to provide stability to thecontroller.

In the feedback controller tuning step 30, the various parametersassociated with the feedback controller of the mass flow controller aretuned to provide satisfactory dynamic response to a series of fluidsteps provided to the mass flow controller. It should be appreciatedthat each implementation of a mass flow controller may have a differentmethod of control (e.g., GLL, PID, ID, etc.). One exemplary procedurefor tuning a feedback controller of a mass flow controller is nowdescribed with respect to the GLL controller depicted in FIG. 4.

In step 32, the reciprocal gain term G formed from the measurements madein step 20 is applied to the GLL controller. In step 34, fluid steps areprovided to the mass flow controller by stepping the set point. Forexample, SI₂ in FIG. 1 is modified by a set of different changes in setpoints ΔS_(i). The different ΔS_(i) may be chosen such that thecontroller is tuned appropriately for large step changes (e.g., a ΔS_(i)of 100% of full scale flow) and small step changes (e.g., a ΔS_(i) of 5%of the full scale flow). The number and magnitude of the various ΔS_(i)may differ for each implementation and according to the differingoperating requirements of a particular mass flow controllerimplementation.

In step 36, the various parameters of the GLL controller are set suchthat the GLL controller responds satisfactorily to the different changesin set point as defined by the various ΔS_(i). For example, parametersincluding the PID constants K_(p), K_(i), etc., may be tuned to providea desired response to changes in set point. Various characteristics ofthe controller that may be tuned include, but are not limited to, risetime, maximum overshoot/undershoot, settling time, etc.

In calibration step 40, having tuned the sensor and controller for adesired dynamic response, and having obtained the composite gain CDA′for various set points, the mass flow controller undergoes a calibrationstep to ensure that the mass flow controller has a satisfactorysteady-state response. The mass flow controller is calibrated, in part,such that the relationship between actual fluid flow and indicated flowis linear. In addition, configuration data may be obtained thatfacilitates the configuration of the mass flow controller on a processfluid and/or process operating conditions as described in calibrationstep 40 of FIG. 7 b.

In step 41 of calibration step 40, a full scale range is defined for themass flow controller. According to one embodiment, the actual fluid flowis measured corresponding to a sensor output of 1.0. An approximatelinearization curve is provided such that at the defined full scaleflow, indicated flow will have a value at or near 1.0. The approximatelinearization curve is then applied to the flow meter 110. It should beappreciated that the values of 1.0 for maximum sensor output andindicated flow are exemplary and may be replaced with any desirednumber.

In step 43, a first set point _(cb)S₀ is chosen from a set of selectedset points {_(cb)S₀, _(cb)S₁, _(cb)S₂, . . . } and applied to the massflow controller. The actual fluid flow in the flow path (e.g., flow path103) resulting from the set point is then measured. Corresponding toeach set point, the sensor output and actual fluid flow are recorded. Itshould be appreciated that fractional flow (i.e. actual fluid flowdivided by the full scale range associated with the test fluid) may berecorded instead of actual fluid flow if more convenient, and that therelevant information is present in both representations. Steps 41 and 43are then repeated for each of the sets points _(cb)S_(i) in the set ofselected set points, resulting in a set of point pairs {sensor output,actual fluid flow}_(i) that may be stored as configuration data asillustrated in step 44 and 45.

The relationship between the point pairs {sensor output, actual fluidflow}_(i) describes the non-linearities associated with the sensor andbetween the proportion of fluid flowing through the sensor conduit andthrough the mass flow controller at different flow rates. Accordingly, alinearization curve may be determined from these point pairs in order toensure that the relationship between fluid flow and indicated flow islinear. In one embodiment, a set of points that corrects for thenon-linearities associated with point pairs {sensor output, actual fluidflow}_(i) is determined. A cubic spline is fit to the set of points suchthat a linearization curve that is continuous and passes through thepoint (0,0) (i.e., fluid flow=0 and sensor output=0) is provided. Instep 46, the linearization curve is applied to the mass flow controller.It should be appreciated that a number of other curve fit methods mayalternatively be used, including, but not limited to, piece-wise linearapproximation, polynomial approximation, etc.

During steps 10-40, configuration data has been recorded from thevarious production steps of the mass flow controller on a test fluid andtest operating conditions. The configuration data contains informationthat facilitates configuration of the mass flow controller for operationwith a process gas and/or process operating conditions. It should beappreciated that the set of configuration data recorded during a manualtuning of a mass flow controller may differ depending on the particularimplementation of the mass flow controller, and may differ from thatillustrated in FIGS. 7 c and 7 d. Accordingly, configuration data forany particular implementation of a mass flow controller merely describesdata obtained during production of a mass flow controller thatfacilitates the configuration of the mass flow controller for operationwith a process fluid and/or process operating conditions.

For example, in the embodiment illustrated in FIGS. 7 c and 7 d, theconfiguration data recorded during steps 10-40 includes sensor tuningparameters, the single gain from the sensor tuning step, tuningconditions, calibration conditions, a set of point pairs {sensor output,CDA′}_(i), a set of point pairs {sensor output, actual fluid flow}_(i),and a full scale range for the test fluid.

In the valve characterization step 20, the point pairs {sensor output,CDA′}_(i) were recorded. As discussed above, the composite gain termCDA′ is the product of the gain terms associated with the valveactuator, the valve and the flow meter, respectively. However, theindividual contributions of gain terms C, D and A′ to the composite gainterm CDA′ are unknown. Also, it is noteworthy that A′ is only a portionof the total gain term A associated with the flow meter.

In system gain decomposition 50, the individual gain terms thatcontribute to the composite gain term CDA′ are isolated from thecomposite gain term in order that they may be determined for a processfluid and/or process operating condition in the succeeding systemconfiguration step 60. However, it should be appreciated that steps51-56 may not be necessary for certain implementations of a mass flowcontroller where, for instance, an accurate model of a valve actuator isavailable, or the gain associated with the actuator for a set of processoperating conditions may be directly obtained. As discussed above,system gain decomposition 50 provides a more general method of modelingthe behavior of the valve actuator (e.g., a method of obtaining gainterm C for a set of process operating conditions.)

In step 51 gain term A is determined. In the previously describedembodiment, the flow meter has been tuned and/or calibrated such that25% of full scale flow results in an indicated flow of 0.25, 50% of fullscale flow results in an indicated flow of 0.5, 75% of full scale flowresults in an indicated flow of 0.75 etc. The relationship between thefluid flow in the flow path and the indicated flow is linear, hence thegain associated with the flow meter (i.e., gain A) is a constant.

Accordingly, gain A can be directly determined in step 51 by dividingindicated flow by fluid flow at any desired point, the simplest beingfull scale flow and the associated indicated flow of 1 ensured by thelinearization curve. Thus, in embodiments wherein the maximum indicatedflow is unity, gain A is equal to the reciprocal of full scale range(i.e., the value of full scale flow through the mass flow controller fora particular fluid species). In general, gain A is equal to the maximumindicated flow value divided by the full scale range associated with aparticular fluid species.

In step 52, composite gain term CDA is formed. Gain term A′ is the gainassociated with the flow meter without the contribution of thelinearization curve while gain term A is a gain associated with the flowmeter including the linearization curve. Therefore, the relationshipbetween A′ and A is by definition the linearization curve. Hence, thecomposite gain term CDA can be directly determined by adding in thecontribution of the linearization curve, which is to say, by multiplyingCDA′ by the gain term associated with the linearization curve (e.g.,multiplying CDA′ by the derivative of the linearization curve). In eachiteration of step 52, gain term CDA_(i) is formed at set point _(d)S_(i)and provided to step 53.

In step 53, the contribution of gain term A is removed. Since both thecomposite gain term CDA and the individual gain term A (the reciprocalof full scale range) are now known, the contribution of gain term A canbe divided out from composite gain term CDA, leaving composite gain termCD associated with the valve actuator and the valve. As illustrated instep 53, gain term CD_(i) is formed at set point _(d)S_(i) and providedto step 54.

As discussed in the foregoing, gain C is the change in valvedisplacement divided by the corresponding change in the drive signal(e.g., DS provided by the GLL controller). Gain D is the change in fluidflow divided by the corresponding change in valve displacement.

In step 54, gain term D is determined and valve displacement iscalculated at a selected set of set points. In order to furtherdifferentiate composite gain term CD, a physical model of the valve isemployed to determine the valve displacement necessary to achieve aparticular fluid flow under a particular set of operating conditions(i.e., to determine gain D). One physical model of the valve that may beused to make this determination is illustrated and described in SectionD. below, entitled “Physical Valve Model”. It should be appreciated thatdifferent valves and valve types may have different physical models.Furthermore, there may be more than one physical model that may be usedto model the characteristics of any particular valve. Accordingly, thepresent invention is not limited to any particular valve model.

In one embodiment, gain D is determined by calculating the valvedisplacement necessary to achieve each fluid flow represented by a setof selected set points {_(d)S₀, _(d)S₁, _(d)S₂, . . . }. A deviation nmay be chosen and the gain term D determined by calculating the valvedisplacement at _(d)S_(i)−n and _(d)S_(i)+n and forming the ratio ofchange in set point to change in valve displacement (e.g.,2n/Δdisplacement). Additionally, the displacement at _(d)S_(i) may bedetermined or the values of displacement at _(d)S_(i)−n and _(d)S_(i)+naveraged in order to determine a displacement_(i) at _(d)S_(i). Asillustrated, in each iteration of step 54, gain term D_(i) and thedisplacement_(i) of the valve at set point _(d)S_(i) are determined.

In step 55, gain term D is divided out of composite gain term CD, thusisolating gain term C. In addition, a set of point pairs {C,displacement}_(i) is generated to provide a model of the behavior of theactuator with the set of test operating conditions used duringproduction 710. It is known that gain term C (the gain associated withthe valve actuator) is not usually directly dependent on process fluidand/or process operating conditions, though it may be a function ofvalve displacement. In each iteration of step 55, the gain term C_(i) isformed by removing the contribution of gain term D_(i) for displacementcalculated at set point _(d)S_(i) and stored in the set {C,displacement}_(i)

Steps 52-55 are repeated for each of the selected set points _(d)S_(i)such that a set of points pairs {C, displacement}_(i) is generated thatprovides information about the behavior of the valve actuator under theset of test operating conditions to the succeeding configuration step.

In system configuration step 60, control parameters are determined for aprocess fluid and/or process operating conditions. The physical modelconsiders fluid species, inlet and outlet pressure, temperature, etc.Accordingly, gain D can be calculated for a process fluid and/or processoperating conditions by providing the fluid species information andprocess operating conditions to the physical model and calculating thedisplacements necessary to achieve the various representative fluid flowvalues. From the displacements determined from the physical model of thevalve and model of the behavior of the valve actuator, gain term C maybe calculated for the process fluid and/or process operating conditions.In one embodiment, the model of the behavior of the actuator is thepoint pairs {C, displacement}_(i) generated in system gain decompositionstep 50. However, in embodiments where the behavior of the valve isknown or can be directly measured, gain C can be directly determinedfrom the valve. Thus, having obtained both gain terms C and D, thecomposite gain term CD may be formed. Subsequently, gain A can becalculated by determining a full scale range for the process fluid.Accordingly, the system gain term CDA can be determined for the processfluid and/or process operating conditions.

The reciprocal of the system gain term may be formed and applied to acontrol loop of a GLL controller (e.g., gain term G). It should beappreciated that G may be a function of one or more operating conditionsof the mass flow controller, such as set point, inlet and/or outletpressure, temperature, etc. Reciprocal gain term G may be applied to theGLL controller such that the control loop of the mass flow controllerhas a constant loop gain with respect to at least the one or moreoperating conditions of which G is a function. Hence, the mass flowcontroller has been configured to operate on a process fluid and/orprocess operating conditions, as discussed further in detail below.

In step 61, a full scale range associated with a process fluid withwhich the mass flow controller is to be configured is determined. Onemethod of determining full scale range is to calculate a conversionfactor based on the specific heat ratios of the process fluid and thetest fluid times the full scale range associated with the test fluid. Itshould be appreciated that other methods may be appropriate forcalculating a full scale range associated with a particular processfluid. For example, the full scale range associated with a particularprocess fluid may be directly measured if appropriate.

In step 62, gain term D is determined for a process fluid and/or processoperating conditions from a physical model of the valve by applyingprocess fluid species information and/or process operating conditions tothe physical model and calculating the displacement necessary to achievea set of representative flow values {_(cf)S₀, _(cf)S₁, _(cf)S₂, . . . }.As discussed above, gain D may be determined by choosing a deviation nand calculating the valve displacement at _(cf)S_(i)−n and _(cf)S_(i)+nand forming the ratio of change in set point to change in valvedisplacement (e.g., 2n/Δdisplacement). Additionally, the displacement at_(cf)S_(i) may be determined or the values of displacement at_(cf)S_(i)−n and _(cf)S_(i)+n averaged in order to determine adisplacement_(i) at _(cf)S_(i). Accordingly, in each iteration of step62, gain term D_(i) and displacement of the valve at set point_(cf)S_(i) are determined for the process fluid and/or process operatingconditions.

In step 63, gain term C is determined for a process fluid and/or processoperating conditions. In some embodiments of the present invention gainC may be directly measured from the actuator itself. Alternatively, gainterm C may be determined from the information stored in the point pairs{C, displacement}_(i) generated in system gain decomposition step 50. Ineither case, in each iteration of step 63, C_(i) is determined atdisplacement_(i) corresponding to set point _(cf) _(S) _(i) for theprocess fluid and/or operating conditions.

In step 64, gain term D is multiplied with gain term C to producecomposite gain term CD. As illustrated, in each iteration of step 64,the product of gain term C_(i) from step 53 and gain term D_(i) fromstep 52 is taken to form composite gain term CD_(i) at set point_(cf)S_(i.)

In step 65, the contribution of gain term A is removed. Since gain termA is simply the reciprocal of full scale range, composite gain term CDcan be divided by the process full scale range associated with theprocess fluid to form system gain term CDA. As illustrated, in eachiteration of step 65, composite gain term CD_(i) is divided by the fullscale range to form system gain term CDA_(i) at set point _(cf)S_(i.)

In step 66, the reciprocal of system gain term CDA is calculated to formreciprocal gain term G. As illustrated, in each iteration of step 66,the reciprocal CDA_(i) is formed and the resulting G_(i) at set point_(cf)S_(i) is provided to block 67 to form reciprocal gain term G. Itshould be appreciated that gain term G may be represented by any numberof techniques. For example, a curve may be fit to the points G_(i), thepoints G_(i) may be stored in a look-up table, or gain term G may berepresented in any manner discussed above in connection with thedefinition of a gain term, or otherwise. In addition, gain term G may bea function of one or more operating conditions. In the embodimentillustrated in FIG. 7 f, gain term G is a function of set point.However, gain G may additionally be a function of more than oneoperating condition depending on the needs of a particularimplementation of a mass flow controller.

Steps 62-66 are repeated for each of the selected set points {_(cf)S₀,_(cf)S₁, _(cf)S₂, . . . } in order to determine reciprocal gain term Gfor the process fluid and/or process operating conditions with which themass flow controller is being configured to operate.

In step 68 reciprocal gain term G is applied to a control loop of themass flow controller to provide a constant loop gain with respect to atleast set point. In general, gain term G will provide a constant loopgain with respect to at least the operating conditions for which it is afunction.

It should be appreciated that by determining the system gain of the massflow controller based on information for the process fluid and/orprocess operating conditions, and by applying a reciprocal gain term ofthe system gain to a control loop of the mass flow controller, the massflow controller has been configured for operation with the process fluidand/or process operating conditions. In other words, the mass flowcontroller will exhibit the same response observed after production ofthe mass flow controller with a test fluid and test operating conditionswhen operating with the process fluid and/or process operatingconditions, that is to say, the mass flow controller, when operatingwith the process fluid and/or process operating conditions, will exhibita satisfactory response.

It should be appreciated that the process of configuring a mass flowcontroller may be automated through the use of a computer. For example,steps 50 and 60 may be controlled entirely by a program stored in memoryand executed on a processor of a computer, such as a personal computer.Hence, a mass flow controller may be automatically configured foroperation with arbitrary process fluids and/or process operatingconditions.

The term automatic or automatically as used herein applies generally toa state of being enacted primarily by or under the control of a computeror processor. In particular, automatic tasks, steps, processes, and/orprocedures do not require extensive operator involvement or supervision.Accordingly, an automatic configuration of a mass flow controllerdescribes a configuration of a mass flow controller for operation with aprocess fluid and/or process operating conditions that does not requiremanual involvement. Configuration of a mass flow controller under thecontrol of a computer program is to be considered an automaticconfiguration.

It should be appreciated that routine tasks such as connecting a massflow controller to a computer or processor, initiating the execution ofa program, etc. are, in general, done manually. However, such tasks areconsidered routine and may be part of an automatic configuration of amass flow controller.

FIG. 14 illustrates a system that facilitates automatic configuration ofa mass flow controller on arbitrary process fluids and/or processoperating conditions. The system includes a mass flow controller 1000and a computer 800.

The mass flow controller 1000 includes a memory 1002, a processor 1004,and the various components of the mass flow controller 1006 illustratedand described with respect to FIG. 1. The processor is coupled to thememory and may be connected to at least some of the components of themass flow controller. As described above, operation of a mass flowcontroller may be implemented under the control of a processor, suchthat the GLL controller 150 is implemented by the processor 1004. Themass flow controller 100 further includes configuration data 1012obtained during production of the mass flow controller and stored inmemory 1002.

The computer 800 includes a memory 802, a processor 804, an inputdevice, and a program 810 stored in memory 802. The program 810 includesinstructions, that when executed on processor 804, carry out varioussteps involved in configuring a mass flow controller for operation on aprocess fluid and/or process operating conditions (e.g., step 712 inFIG. 7 a, steps 60 and 70 in FIGS. 7 b, 7 e, and 7 f, etc.).

It should be appreciated that computer 800 may be any of a number ofcomputing devices known in the art. For example, computer 800 may be apersonal computer, a laptop, a hand held device, or any other computingdevice capable of executing a program. Furthermore, computer 800 may beconnected to and communicate with the mass flow controller in any numberof ways known in the art. For example, computer 800 may be connected viaa cable using any number of standard communication methods including,but not limited to, standard parallel port communication, serial portcommunication, Universal Serial Bus (USB), etc. Alternatively, thecomputer 800 may have a wireless connection with the mass flowcontroller. Accordingly, it should be appreciated that the presentinvention is not limited to a particular type of computing device, inputdevice, connection type, or communication method, as a variety of typesof computing devices, connection types, and communication methods maysuitably be used.

According to one embodiment of the present invention, the computer 800may be connected to the mass flow controller in order to configure themass flow controller on a process fluid and/or process operatingcondition. The program 810 may then be executed on processor 804.Configuration input may be provided to the input device 808. Theconfiguration input may include, but is not limited to, process fluidspecies information, process operating conditions, and/or otherinformation relevant to the configuring of the mass flow controller. Theinput device may be any of a number of devices capable of receivinginformation, including, but not limited to, a keyboard or keypad,interface software for receiving input from a mouse, pointer, etc.

The program 810 may then obtain configuration data 1012 stored in memory1002 of the mass flow controller. From the configuration data andconfiguration input, program 810 determines control parameters for themass flow controller that facilitate operation of the mass flowcontroller with the process fluid and/or process operating conditions.The program 810 may then apply the control parameters to the mass flowcontroller by either modifying existing control parameters accordingly,or by adding additional control parameters to the mass flow controller.In this manner, the mass flow controller may be automatically configuredfor operation with the process fluid and/or process operatingconditions.

In an alternative embodiment illustrated in FIG. 15, the program 810 maybe stored in memory 1002 of the mass flow controller and may be executedon processor 1004 which may also be used to implement the GLL controller150. An input device 1008 may be added to the mass flow controller toenable the mass flow controller to receive configuration input.Accordingly, the mass flow controller 1000 illustrated in FIG. 15 isauto-configurable.

C. Hysteresis Reduction

It is often the case that mass flow controllers experience instabilityassociated with the operation of its individual components. For example,mass flow controllers employing solenoid actuated valves are susceptibleto imprecision due to hysteresis effects associated with the magneticsof the solenoid.

One embodiment of the present invention provides a method of reducinghysteresis in a solenoid device by applying a non-operational signal toa solenoid actuated device.

The term non-operational signal, when applied to solenoid actuateddevices, describes a signal applied to the device that is incapable ofactuating the device. For instance, in a solenoid actuated valve, anon-operational signal may refer to a signal having insufficientmagnitude to displace the controlled portion of the valve (i.e., theplunger). It should be appreciated that the non-operational signal maybe the same signal as the control or drive signal of the device onlyreduced such that it is insufficient to actuate the device.

FIG. 8 graphically illustrates the principle of hysteresis in a solenoidactuated control valve of a mass flow controller that is normally in aclosed position (i.e., the default position the valve is closed,referred to herein as a normally closed valve). In FIG. 8, control valvedrive current is plotted along the horizontal axis and fluid flowthrough the control valve is plotted along the vertical axis. AlthoughFIG. 8 is specifically directed to a solenoid actuated control valve ina mass flow controller, it will be appreciated that it is representativeof solenoid actuated devices in general, as the horizontal axisgenerally corresponds to the amount of energy provided to the solenoidactuated device, and the vertical axis generally corresponds topositional displacement of the solenoid actuated device.

As shown in FIG. 8, as valve drive current is increased, the actual flowof fluid through the control valve does not begin to increase untilafter an amount of drive current sufficient to overcome a spring forceof a spring that biases the control valve in a closed position isprovided. The amount of drive current necessary to overcome this springforce is denoted in FIG. 8 by the point X_(i). Under normal operatingconditions, actual fluid flow through the control valve starts toincrease at some point after the point X₂. As shown by the curve labeledC₁, as the valve current is increased beyond the point X₂, the actualflow through the control valve increases in a proportional butnon-linear manner, with the portion of curve C₁ that is labeled R₁representing the typical operating range of a normally-closed controlvalve in a mass flow controller.

Although FIG. 8 is not drawn exactly to scale, the operating range of anormally-closed control valve of a mass flow controller typicallyrepresents a displacement of the control valve from its closed positionof approximately several microns for low-flow mass flow controllers upto several hundred microns for high-flow mass flow controllers. Itshould be appreciated that the operating range will depend on the flowrequirements of a particular mass flow controller.

In the embodiment illustrated in FIG. 8, valve drive currents above thepoint X₃ represent operation of the mass flow controller outside itsoperating range (e.g., the range of mass flow rates over which the massflow controller is designed and/or calibrated to operate), with the fullopen position of the control valve (i.e., above point X₅) representing apurge mode of the mass flow controller in which the displacement of thecontrol valve (from its closed position) is on the order ofapproximately 250 microns for low to moderate flow mass flowcontrollers. It should be appreciated that while the full open positionof the control valve is a position at which the mass flow controller isintended to operate, it is not a position at which the mass flow rate ofthe fluid flowing therethrough can be accurately controlled and/ormonitored. Accordingly, as used herein, when used in connection with amass flow controller, the term operating range is defined to mean thatrange of positional displacement over which the mass flow rate of fluidflowing through the control valve can be accurately controlled andmonitored.

As can be seen in FIG. 8, when the control valve is brought to its fullopen position and then the valve drive current is decreased, the actualflow of fluid through the control valve versus drive current no longerfollows curve C₁, but instead tends to follow a different curve C₂.Thus, as valve current is decreased from the point X₅, the actual fluidflow through the control valve does not begin to decrease untilapproximately point X₆, whereupon the actual flow of fluid versus valvedrive current then decreases in a proportional (but again, non-linearmanner) following curve C₂.

If, after operating the control valve in this manner (i.e., operatingthe control valve first along curve C₁ and then returning the controlvalve to its off position along curve C₂), it is then desired to resumenormal operation, the actual flow of fluid through the control valvedoes not again follow curve C₁, but instead, will follow yet a differentcurve C₃ positioned somewhere between curve C₁ and C₂. In fact, wherecurve C₁ represents a plot of drive current versus actual flow for apreviously unmagnetized solenoid control valve, and curve C₂ represent aplot of drive current versus actual flow for a highly magnetizedsolenoid control valve (e.g., after returning the control valve to itsoff position along curve C₂), the curve C₃ will be positioned moreclosely to curve C₂, as shown. Thus, instead of actual fluid flowcommencing at the point X₂, fluid flow will instead commence at aboutpoint X₇. If the control valve is operated within its normal operatingrange along curve C₃ and returned to a closed position, the next timethat the valve is opened, the actual flow of fluid through the controlvalve versus valve drive current will follow yet a different curve(e.g., curve C₄), which is one of a family of curves between curve C₁and curve C₂. Whether curve C₄ is positioned closer to curve C₁ or tocurve C₂ will depend upon the operation history of the valve includingthe highest point on the curve C₃ at which the control valve is operatedduring that operational cycle. The above-described operation of thecontrol valve in which the present state of operation is dependent uponits prior operating state is termed hysteresis.

Consequently, hysteresis adversely affects the ability to accuratelypredict the drive level at which the valve will first permit flow aftereach operation cycle, as it depends on the operation history of thevalve during the operation cycle. As described above, a pedestal is setto just below the drive level at which the valve will begin to permitflow. However, the uncertainty caused by hysteresis with respect to thatdrive level adversely effects the accuracy with which the pedestal maybe set. Setting the pedestal too high may result in undesirableovershoot. Setting the pedestal too low may result in a slow responsetime when transitioning from zero flow to controlled flow.

FIGS. 9-13 graphically illustrate a number of different waveforms thatmay be used as non-operational signals to reduce the effect ofhysteresis in a solenoid actuated device. Each of these non-operationalsignals may be provided as a drive signal to the solenoid actuateddevice. For example, in the mass flow controller of FIG. 1, suchnon-operational signals may be provided by the GLL controller 150 to thevalve actuator 160 to reduce hysteresis.

With reference to FIG. 9, a time-varying sinusoidal signal may beprovided to a solenoid actuated valve or other device to mitigate theeffects of hysteresis. As shown in FIG. 9 a sinusoidal wave form may beprovided that diminishes in the amplitude over a time period T_(i).Where the solenoid actuated device is a control valve of a mass flowcontroller, the amplitude of the sinusoidal signal should be less thanthe amount of current that is needed to open the solenoid actuatedvalve. For example, in a mass flow controller that utilizes a normallyclosed position solenoid actuated valve, the maximum value of thenon-operational signal should be less than the minimum amount of currentneeded to overcome the spring force and open the valve. Thus, referringback to FIG. 8, the maximum value of the signal would be less than X₁ toensure that no fluid can pass through the valve during the provision ofthe waveform.

As illustrated in FIG. 9, the time varying waveform diminishes inamplitude over a time period T₁. Empirical results have demonstratedthat a waveform of approximately 10 to 20 cycles is sufficient toprecondition a typical solenoid actuated valve to a predetermined state,regardless of its prior state of operation (i.e., whether it wasoperated within its normal operating range or outside the normaloperating range such as in a purge mode). Where the solenoid actuatedcontrol valve is a valve that is normally in an open position, thewaveform should be such that the valve is in a closed positionthroughout the procedure to prevent the flow of fluid through the valve.

In general, the frequency chosen for a particular waveform may depend onvarious constraints of an implementation. For example, the frequencythat can be delivered to the solenoid actuated device may be limited bypower constraints. Additionally, a lower bound may be imposed on thefrequency by the time that the solenoid actuated device may remainclosed. However, in general any frequency within the constraints of aparticular implementation that provides a desired number of cycles issuitable. For example, a signal provided in the range between 10-20cycles has been shown to produce a reduction in the effects ofhysteresis described herein, however, said range is not limiting.

Although it is believed that the time varying waveform illustrated inFIG. 9 is best suited to reducing the effects of hysteresis in asolenoid actuated device, empirical results have determined that avariety of other waveforms may be used to set the solenoid actuateddevice to a predetermined state. Generally, each of these waveformsprovide a time varying signal to the solenoid actuated device thatdiminish in amplitude over time. However, empirical results have alsodemonstrated that it is not necessary to use a time varying waveformthat diminishes in amplitude, as a constant amplitude time varyingsignal may also be used.

FIG. 10 illustrates another time varying current waveform that may beused to reduce or eliminate magnetically induced hysteresis in asolenoid actuated control valve or other solenoid actuated device. As inFIG. 9, the time varying waveform diminishes in amplitude over a timeperiod T₁ and has a maximum amplitude that is less than the magnitude ofthe control signal necessary to permit fluid to pass through the valve.As with the time varying waveform of FIG. 9, the time period T₁ may beon the order of approximately 1 second to avoid interfering with normaloperation. However, rather than a sinusoidal waveform, a square waveformis provided. Based upon empirical testing, it is believed that othertime-varying waveforms may be provided, such as saw-tooth wave forms,etc. It should be noted that each of the waveforms illustrated in FIGS.9 and 10 is capable of providing positive and negative values to thesolenoid actuated device. In general, such a waveform that includes bothpositive and negative values is preferred for setting the solenoidactuated device to a predetermined state, as it effectively dischargesthe residual magnetism of the magnetic core of the solenoid actuateddevice imposed during operation.

FIGS. 11 and 12 show alternative waveforms that may be used to reduce oreliminate hysteresis in a solenoid actuated control valve. The waveformillustrated in FIG. 11 again has a diminishing amplitude over a timeperiod T₁. However, in contrast to the waveform illustrated in FIGS. 9and 10, the time varying waveform depicted in FIG. 11 includes onlypositive values. Depending upon the particular circuit in which thesolenoid actuated control valve is used, one may not have the ability toprovide a signal that assumes both positive and negative values.

FIG. 12 illustrates a time variant waveform that may also be used toreduce or eliminate hysteresis in a solenoid actuated control valve.Although a triangle-shaped waveform is illustrated, it should beappreciated that a sinusoidal waveform, a square wave, or a number ofalternatively shaped waveforms may be used.

It should be appreciated that in each of FIGS. 9-12, the maximumamplitude of the time varying waveform is such that it is incapable ofactuating the solenoid actuated control valve, as the maximum amplitudeis less than the magnitude of the control or drive signal required toovercome the spring force and open the valve. Applicants have found thattime variant current wave form illustrated in FIG. 12 is easily providedwith existing components used in a mass flow controller and does notrequire any additional circuitry. Moreover, other time varying waveformsmay also be provided, such as a square wave, a triangle, or a sawtoothshaped waveform.

As discussed above, it should be appreciated that the frequency andduration with which a waveform is provided to the solenoid actuateddevice is not limited to values used herein as examples to illustratesome values that both provide a suitable number of cycles and do notinterfere with normal operation of the solenoid actuated device. Othervalues are suitable and are considered to be within the scope of theinvention.

FIG. 13 illustrates an alternative waveform that may be used to set asolenoid actuated device to a particular predetermined state after eachcycle of operation. As shown in FIG. 13, a negatively valued pulse isapplied to the coil of the solenoid actuated valve. When used inconjunction with a mass flow controller, the sign of the pulse shouldordinarily be opposite to that which is normally used to open or purgethe solenoid actuated control valve, and of a magnitude that isincapable of activating the valve. For example, with a normally closedsolenoid actuated control valve, this would correspond to the negativegoing pulse. It should be appreciated that the pulse of current that isapplied should be such that it is opposite in polarity to that requiredto purge the mass flow controller. In the case of solenoid actuateddevice in general, the pulse should be of a polarity that is incapableof actuating the solenoid actuated device, and preferably one that isopposite to the polarity of the normal drive signal.

It should be appreciated that the non-operational signal can be acurrent, voltage or otherwise. Accordingly, the waveforms illustrated inFIGS. 9-13 and described herein are considered to be time varyingwaveforms of the particular form used in any particular implementation(e.g., a time varying current waveform, a time varying voltage waveformetc.).

Each of the above described drive signal waveforms is capable of settinga solenoid actuated device, such as a control valve to a predeterminedstate. Accordingly, referring back to FIG. 8, it is known to which curveC that the actuated device will operate on. Thus, imprecision due to theoperation of the device on any of a family of curves C_(i) is reduced oreliminated.

It should be appreciated that while it may not be necessary to set thesolenoid actuated device to the predetermined state after each cycle ofoperation, it is preferable to do so. For example, even if the solenoidactuated device has not been operated outside its normal operatingrange, the solenoid actuated device may still be affected by hysteresisdue to the history of operation of the device within its normaloperating range. In addition, because detecting when the solenoidactuated device is operated outside of its normal operating range canrequire additional code and/or detection circuitry, it is generallypreferred to set the solenoid actuated device to the same predeterminedstate after each cycle of operation, irrespective of whether the priorcycle was within or outside the normal operating range. In this manner,the solenoid actuated device will be conditioned to follow a particularcurve during operation, irrespective of its prior state of operation.

It should be appreciated that non-operational signals may be provided ina number of ways and the present invention is not limited to anyparticular implementation. For example, various waveforms (e.g., thewaveforms illustrated in FIGS. 9-13) may be generated by the control andcontrol electronics of a mass flow controller (e.g., GLL controller 150)and converted into a non-operational signal by the valve actuator andprovided to the valve in order to reduce hysteresis. Alternatively, afunction generator may be coupled to the valve or valve actuator inorder to provide a non-operational signal to reduce hysteresis.Waveforms generated by any suitable means may be in digital or analogform and may be converted appropriately according to the needs of aparticular implementation. Indeed, many techniques for generatingsuitable signals are known in the art and are considered within thescope of the present invention.

D. Physical Valve Model

According to another aspect of the present invention, Applicants havephysically modeled the flow of fluid at different inlet and outletpressures as predominately consisting of two components: the viscouspressure drop and the inviscid (dynamic) pressure drop. By summing thecontributions of each of these components where the effectivedisplacement of the valve for each component is equal, the effectivedisplacement of the valve may be empirically determined using thefollowing methodology. As noted above, the determination of theeffective displacement of the valve at a particular fluid flow rate on aparticular fluid enables the gain term associated with the valve (e.g.,gain term D) to be determined, and thus the determination of the gainterm associated with the valve actuator (e.g, gain term C).

Referring to FIG. 16, allowing the upstream or inlet pressure to berepresented by P₁ and the downstream or outlet pressure to berepresented by P₂, then at a mass flow rate represented by Q, thevalve-lift is represented by H, and the viscous effect alone reduces thepressure from P₁ to some intermediate pressure P_(x). The inviscidcompressible flow further reduces the pressure from an intermediatepressure P_(x) to P₂. Modeling the viscous pressure drop across thevalve 170 based upon a physical model of viscous flow of fluid betweentwo parallel plates (e.g., between the valve seat and the jet surface),the distance H between the two parallel plates (e.g., the displacementof the valve 170) is provided by the following equation: $\begin{matrix}{H^{3} = {{\frac{{24 \cdot \mu}\quad{QLRT}}{w\left( {P_{1}^{2} - P_{x}^{2}} \right)} \cdot 1.654} \times 10^{- 18}\quad\left( {ft}^{3} \right)}} & \left( {{equation}\quad 1} \right)\end{matrix}$

where:

P₁, P_(x): Pressure upstream and downstream of the viscous surface(psi);

Q: Mass flow rate (sccm);

L: length of the flow path (ft);

H: distance between the two parallel surfaces (ft);

w: the breadth of the flow path, w equals π·ø, and ø is the meandiameter of plateau 1650, ø is equal to 0.040″ based upon the testedvalve;

μ: dynamic viscosity of the gas (centi-Poise);

T: Absolute temperature (deg. Rankine);

{circumflex over (R)}: universal gas constant, 1545.33(ft-lbf/lb-mole-deg. R); and

R: gas constant (ft-lbf/lbm-deg. R).

Modeling the inviscid pressure drop across the valve 170 based upon aphysical model of inviscid flow of fluid through an orifice or jetprovides $\begin{matrix}{\frac{Q}{A} = {1.2686 \times 10^{6}\quad{P_{x,0}\left( \frac{2}{\gamma + 1} \right)}^{(\frac{\gamma + 1}{2{({\gamma - 1})}})}\sqrt{\frac{\gamma}{M_{w}T_{1,0}}}}} & \left( {{equation}\quad 2} \right)\end{matrix}$

for choked flow; and: $\begin{matrix}{\frac{Q}{A} = {1.2686 \times 10^{6}\quad{P_{x,0}\left( \frac{P_{2}}{P_{x,0}} \right)}^{(\frac{\gamma + 1}{2\quad\gamma})}\sqrt{\frac{2\quad\gamma}{\left( {\gamma - 1} \right)\quad M_{w}T_{1,0}}\left\{ {\left( \frac{P_{x,0}}{P_{2}} \right)^{(\frac{\gamma - 1}{\gamma})} - 1} \right\}}}} & \left( {{equation}\quad 3} \right)\end{matrix}$

for unchoked flow; where the flow is choked if $\begin{matrix}{\frac{P_{2}}{P_{x,0}} \leq \left( \frac{2}{\gamma + 1} \right)^{(\frac{\gamma}{\gamma - 1})}} & \left( {{equation}\quad 4} \right)\end{matrix}$

and unchoked otherwise, and where

Q=flow through the valve (sccm);

A=π·ø·H=valve effective area (sq. in,);

ø=diameter of orifice 1640;

M_(w)=gas molecular weight (gm/mol);

P_(x,0,)=upstream total pressure (torr);

P₂=downstream static pressure (torr);

T_(1,0)=gas temperature (K);

γ=ratio of specific heats.

From the above viscous and inviscid equations, the effectivedisplacement (i.e., H) of the valve 170 may be readily determined.Although some of the units used for the above inviscid calculationsappear to be different from those used in the viscous calculation, thereare no generic difference between the equations and the unit conversionfactors were already built into the numerical constants in eachequation.

To determine the effective displacement of the valve, assuming themeasured mass flow rate to be Q and the measured upstream and downstreampressure to be P₁ and P₂ respectively, and neglecting the contributionof the velocity head to the total pressure, a method of calculating theeffective displacement of the valve 170 may be performed. One exemplarymethod of calculating the effective displacement is to estimate theintermediate pressure Px by trial-and-error, where one calculates thevalues of H from both the viscous flow theory (Hv, Eq. 1) and theinviscid theory (Hi, Eq. 2 or 3), depending on whether the flow ischoked or not, (Eq. 4). Thus, if the intermediate pressure isapproximately twice the outlet pressure, choked flow may be assumed, andequation 2 is used for the inviscid component of the calculation,whereas if the inlet pressure is less than approximately twice theoutlet pressure, equation 3 is used for the inviscid component of thecalculation. For a given Q, P1, and P2, the correct Px is obtained whenHv and Hi become equal to each other. Thus, the computational schemeinvolves successive iteration to obtain P_(x). The calculation begins bychoosing P_(x) to be mid-way between P₁ and P₂. Then the viscousvalve-lift (Hv) and the inviscid valve-lift (Hi) are calculated. If itis determined that Hv is greater than Hi, meaning that there is notenough differential pressure for the viscous flow to deliver therequired flow than for the inviscid flow, then during the next iterationa somewhat lower pressure P_(x)′ will be chosen, i.e., between thedownstream pressure P₂ and the previous pressure P_(x). The iterationcontinues until the two calculated valve-lift Hv and Hi come within 0.1%of each other. According to a further aspect of the present invention,this iterative process may be performed in software. The software forperforming this iterative calculation may readily be performed by one ofordinary skill in the art and implemented on a computer. Accordingly,based upon the above method, the effective displacement of the valve 170may be determined for each of a number of different flow rates.

As discussed previously, based upon empirical testing with a variety ofdifferent fluids or gases, Applicants have determined how the fractionalcontribution of the gain A of the mass flow meter changes from one gasto another, as it is primarily dominated by the specific heat of thefluid or gas being used. Accordingly, once the mass flow controller 100has been calibrated with a known fluid or gas, how this gain changes forother types of gases is known. Further, the fractional contribution ofthe gain B of the GLL controller 150 is known to the mass flowcontroller 100, as the various constants that determine this gain may bestored in a memory of the mass flow controller 100, and the fractionalcontribution of the gain C of the valve actuator 160 is effectivelyconstant or known. Accordingly, what remains is a way of determining howthe fractional contribution of the gain D of the valve 170 and gas pathchanges for different gases and for different operating conditions, andhow to compensate for changes in the range of the mass flow controller100 for a different fluid or gas than that with which the mass flowcontroller 100 was initially calibrated.

According to a further aspect of the present invention, a method ofconfiguring a mass flow controller that has been tuned at under knownconditions and with a known fluid or gas is provided that may be used totune the mass flow controller to have a nearly identical response on adifferent fluid or gas, or with a different operating range that thatwith which it was tuned. As discussed above, mass flow controller 100 isinitially tuned on a known gas (for example, Nitrogen) with a knowninlet pressure and a known outlet pressure. For simplicity, oneembodiment of the present invention selects the known inlet pressure tobe greater than two atmospheres and the outlet pressure at ambient. Thisselection of inlet and outlet pressure is advantageous for two reasons.First, use of inlet and outlet pressures relating to choked flowfacilitate the physical modeling of the valve and valve gas path, asonly choked flow conditions can be used for the inviscid pressure dropequations. Second, this type of operation (i.e., a pressure drop ofapproximately two atmospheres) is typical of the type of operation usedby end-users. Under these conditions, the gain of the gas path may bedefined as: $\begin{matrix}{{gain} = \frac{\left( {{change}\quad{of}\quad{gas}\quad{flow}} \right)/\left( {{full}\quad{scale}\quad{flow}\quad{range}} \right)}{\left( {{change}\quad{of}\quad{valve}\quad{drive}} \right)/\left( {{Max}\quad{valve}\quad{drive}} \right)}} & \left( {{Equation}\quad 5} \right)\end{matrix}$

To operate this same mass flow controller on gas “x” with a newfull-scale flow range, the closed-loop gain of the mass flow controller100 may be expected to change as follows: $\begin{matrix}{\frac{{new}\quad{gain}\quad{on}\quad{gas}\quad x}{{old}\quad{gain}\quad{on}\quad N_{2}} = \quad{\left( \frac{1}{{Cfc}_{x}} \right)^{0.4}\quad\left( \frac{{Mw}_{N2}}{{Mw}_{x}} \right)^{0.2}\quad\left( \quad\frac{{old}\quad N_{2}\quad{range}}{{new}\quad N_{2}\quad{range}}\quad \right)}} & \left( {{equation}\quad 6} \right)\end{matrix}$

-   -   where Cfc_(x)=conversion factor “C” for gas x    -    Mw=molecular weight of gas

The above equation is approximate, as there is an additional term whichis a function of inlet pressure, temperature, and the ratio of specificheats. However, the effect of this additional term is to the 0.4 powerand can normally be neglected. For example, assuming that thecalibration of the mass flow controller 100 was initially performed withNitrogen as the known fluid or gas, the value of this additional termranges from 0.684 for Nitrogen and other diatomic gases, up to 0.726 formonatomic gases, and down to 0.628 for polyatomic gases, then raised tothe 0.4 power. Thus, the difference from Nitrogen is at most about 3.5%and may ordinarily be neglected. To compensate for the above change ingain with a different gas and or different operating conditions thanthose used in calibration, the gain term G may be changed by the inverseof the above ratio to provide a constant closed-loop gain for the massflow controller, irrespective of set point, irrespective of operatingconditions, and irrespective of the type of fluid or gas that is used.That is, if the closed-loop gain of the mass flow controller is A*B*C*D,then the gain term G is set to a constant time 1/(A*C*D) to provide aconstant closed-loop gain that is the same as that used duringcalibration.

Having described several embodiments of the invention in detail, variousmodifications and improvements will readily occur to those skilled inthe art. Such modifications and improvements are intended to be withinthe scope of the invention. Accordingly, the foregoing description is byway of example only, and is not intended as limiting. The invention islimited only as defined by the following claims and the equivalentsthereto.

1. A method of determining a displacement of a valve having a valveinlet to receive a flow of fluid at an inlet pressure and a valve outletto provide the flow of fluid at an outlet pressure, the methodcomprising acts of: (A) selecting an intermediate pressure between theinlet pressure and the outlet pressure; (B) determining a firstdisplacement of the valve based upon a viscous pressure drop from theinlet pressure to the intermediate pressure; (C) determining a seconddisplacement of the valve based upon an inviscid pressure drop from theintermediate pressure to the outlet pressure; (D) determining whetherthe first displacement is approximately equal to the seconddisplacement; and (E) selecting, one of the first displacement and thesecond displacement as the displacement of the valve when the firstdisplacement is approximately equal to the second displacement.
 2. Themethod of claim 1, further comprising an act of: selecting a newintermediate pressure when it is determined in act (D) that the firstdisplacement is not approximately equal to the second displacement. 3.The method of claim 2, further comprising an act of: repeating acts(B)-(D) until it is determined in act (D) that the first displacement isapproximately equal to the second displacement.
 4. The method of claim3, wherein the act (C) includes acts of: using a first calculation,based upon the inviscid pressure drop from the intermediate pressure tothe outlet pressure under choked flow conditions, to determine thesecond displacement when the intermediate pressure is approximately twotimes greater than the outlet pressure; and using a second calculation,based upon the inviscid pressure drop from the intermediate pressure tothe outlet pressure under non-choked flow conditions, to determine thesecond displacement when the intermediate pressure is less thanapproximately two times greater than the outlet pressure.
 5. The methodof claim 4, wherein the first and second calculations are based upon aphysical model of inviscid flow through an orifice.
 6. The method ofclaim 5, wherein the act (B) includes an act of: using a firstcalculation that is based upon a physical model of viscous flow betweentwo parallel plates to determine the first displacement of the valve. 7.The method of claim 3, wherein the inlet pressure is at or greater thanapproximately two atmospheres and the outlet pressure is at or belowambient, and the act (C) includes an act of: using a first calculation,based upon the inviscid pressure drop from the intermediate pressure tothe outlet pressure under choked flow conditions, to determine thesecond displacement.
 8. The method of claim 1, wherein the act (C)includes acts of: using a first calculation, based upon the inviscidpressure drop from the intermediate pressure to the outlet pressureunder choked flow conditions, to determine the second displacement whenthe intermediate pressure is approximately two times greater than theoutlet pressure; and using a second calculation, based upon the inviscidpressure drop from the intermediate pressure to the outlet pressureunder non-choked flow conditions, to determine the second displacementwhen the intermediate pressure is less than approximately two timesgreater than the outlet pressure.
 9. The method of claim 8, wherein thefirst and second calculations are based upon a physical model ofinviscid flow through an orifice.
 10. The method of claim 9, wherein theact (B) includes an act of: using a first calculation that is based upona physical model of viscous flow between two parallel plates todetermine the first displacement of the valve.
 11. The method of claim1, wherein the act (C) includes an act of: using a first calculationthat is based upon a physical model of inviscid flow through an orificeto determine the second displacement.
 12. The method of claim 1, whereinthe act (B) includes an act of: using a first calculation that is basedupon a physical model of viscous flow between two parallel plates todetermine the first displacement of the valve.
 13. The method of claim1, wherein the displacement of the valve is determined without physicalmeasurement.